Down the timing rabbit hole
Most questions about resolving simultaneous events ultimately have three options for answers; you can resolve them as decided by the player whose turn it is (XGtE optional rule), you can decide them in Initiative Order (JC tweet unofficial suggested ruling), or you can decide them by DM fiat (Rules 0, 1, and 3). I think this question is a little more complicated than just devolving to one of these three automatically. At the risk of overthinking it, let's explore what is actually happening here.
Is there a conflict?
Before worrying about the order in which to resolve simultaneous events, you should first determine whether there is a conflict between them that will make outcomes different depending on the order. Otherwise, parsing the order is meaningless.
This is the point that Thomas Markov makes in their answer; the order of resolution doesn't matter because "if his destruction is resolved before his regaining hit points, he's destroyed, but if it is resolved after he regains hit points, he is destroyed."
While the general principle is sound, I'm not sure it applies in this case because it makes an assumption about the way events are resolved that, as far as I can tell, we don't actually know to be true. Suppose the Mythic undead is at 0 hp as a result of the mace blow. This will trigger two effects; at 0 hp the Mythic Trait hp regain will trigger and at hp < 26 the mace destruction will trigger. Thomas Markov's argument is that the order of their triggering and resolution doesn't matter, because once the destruction has been triggered, it must be resolved: the creature destruction is coming, and there isn't anything the Mythic Trait can do about it. However, that's not necessarily so. The question is do triggered effects check to see whether they still have valid targets before they resolve? In M:TG, for example, they do check (Rule 608.2b): if multiple triggers are 'on the stack', the resolution of one of them might make the target invalid for a later resolving one, in which case it would not resolve.
In our example, if mace destruction and Mythic trait were both triggered at 0 hp but the destruction resolved first, the Mythic creature would already be dead by the time Mythic Trait resolved, in which case it would fail. But if Mythic Trait resolved first, it might be that by the time the mace destruction event resolved, it would 'check again', see that the target creature had more than 25 hp and had thus become an invalid target, and be canceled without having acted. Or, it might be, as Thomas Markov says, that the mace destruction doesn't care whether the target was still valid by the time it gets to resolve; it is enough that it was valid when it triggered and it will resolve regardless.
As far as I can tell, D&D 5e doesn't have any explicit rules to guide us about such events. We don't even have clear rules on whether an ongoing spell is ended, suppressed, or unaffected when its target is no longer valid.
We shouldn't be surprised that there are no clear rules about this, though. Unlike M:TG, simultaneous effects are typically rare in D&D, and D&D has a full-time arbiter (the DM) whose job it is to decide the many interactions in the game that have been deliberately left vague. Thus, when presented with such a situation, a DM's first decision is whether they want triggered effects to check whether a target is still valid before they resolve. If this is not desired, then the order of these two effects doesn't matter. But if the effects do indeed check their target, then the order they are resolved does very much matter.
Are both effects part of the attack resolution?
Suppose that effects do 'check again' for valid targets before they resolve. Then the order of resolution of these two effects does matter. But before we declare them simultaneous effects, are we sure that they are?
In this example, an attack with a mace of disruption has been made. As stated in the PHB (p. 194), an attack has a simple structure: (1) choose a target, (2) determine modifiers, and (3) resolve the attack. For the third step, we are told:
You make the attack roll. On a hit, you roll damage, unless the particular attack has rules that specify otherwise. Some attacks cause special effects in addition to or instead of damage.
When I first began researching this question, I thought this passage was the answer. The destruction caused by the mace is clearly a 'special effect' of the attack, and should be considered part of the resolution of the attack itself. The Mythic Trait, on the other hand, seemed to happen later, after the resolution of the attack, when the creature 'state-checks' itself, realizes that it is at 0 hp, would go unconscious, but then replaces the unconsciousness effect with the hp regain instead. Thus, I thought, these two effects are not actually simultaneous - the destruction effect of the mace must occur before the effect of the creature being at 0 hp. I have to admit I am still rather sympathetic to this view. Most of the combat section seemed to bear this out - until I re-read the part on Knocking a Creature Out (PHB p. 198):
When an attacker reduces a creature to 0 hit points with a melee attack, the attacker can knock the creature out. The attacker can make this choice the instant the damage is dealt. The creature falls unconscious and is stable.
"The instant the damage is dealt" means that this unconsciousness can also be considered as part of the 'special effects' that happen in step three of making an attack, as part of the resolution of the attack itself. So, is this a case of specific over general, where knocking a creature out is explicitly part of attack resolution, but a creature falling unconscious at 0 hp otherwise occurs later? Or are all instances of damage reducing a creature to 0 hp and the consequences thereof considered part of attack resolution? I'm afraid the rules don't tell us that, either.
Does the mace give us a clue?
If a DM that has gotten this far and decided that two effects are indeed part of resolving the attack, there is a last chance that they are not actually simultaneous. The effects themselves could give a clue as to when they occur. From Mythic Trait:
If [the creature] is reduced to 0 hit points, it doesn’t die or fall unconscious. Instead, it regains [x] hit points.
Clearly this happens when it would otherwise ('instead') fall unconscious.
But from the mace (emphasis mine):
If the target has 25 hit points or fewer after taking this damage, it must succeed on a DC 15 Wisdom saving throw or be destroyed.
That word "after" hints at timing, but unfortunately it gives us more questions than answers. What does 'after taking this damage' mean? Surely it doesn't mean 'at any time after taking this damage', that is, it is not saying that if you hit the undead creature once with the mace and the next day it has less than 26 hp from another attack the destruction would be triggered. A more natural reading is 'immediately after taking this damage', but if that is the intent, why not simply say so - or avoid the ambiguity altogether and say 'If the target has 25 hit points or fewer as a result of taking this damage'. Either one of these more specific triggers would establish that the mace effect is resolved first and the target would be destroyed, Mythic Trait notwithstanding. On the other hand, 'after' could also mean 'after the resolution of the attack', opening up the possibility that another triggered effect, like Mythic Trait, could save the creature. This is in fact, according to Sage Advice 2.0, what allows a Barbarian's Relentless Rage or a Druid's Wild Shape to save them from the disintegration spell: "The disintegrate spell turns you into dust only if the spell's damage leaves you with 0 hit points. If you're a half-orc, Relentless Endurance can turn the 0 into a 1 before the spell can disintegrate you." Is there a general rule about whether such 0 hp triggered effects have to wait until the end of the attack resolution to see the final hp total of their intended target? Unfortunately not, which then leaves the DM in the position of having to determine how much after the 'after' in the mace description means.
The bitter end
Only having made the deliberate decision that the two effects are simultaneous, that the 'after' clause of the mace does not wait for the Mythic Trait to happen, and that the order of resolution of the effects actually matters, do we then have no other option but to make our tripartite choice for resolution: we can resolve these effects as decided by the player whose turn it is (the XGtE optional rule), we can decide them in Initiative Order (the JC tweet unofficial suggested ruling), or we can decide them by DM fiat (Rules 0, 1, and 3).
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Order of resolution of several identical initiative Attacks
Can a reaction interrupt multiattack?
In what order do simultaneously-triggered Opportunity Attacks happen?
Can you apply multiple on-hit effects and if you can, who decides the order they're applied in?
Are there any rules or guidelines about the order of saving throws?