It's unclear, because the wording in the playtest material you are using is off, and it's not clear what the authors may have intended.
Previous editions had clear rules for mixed damage types, but 5E does not — and unlike in previous editions, there isn't anything in the official published rules that has multiple damage types.*
I can't immediately find a designer-intent reference, but this seems to be in line with the general trend towards streamlining and simplifying some of the more complicated rule subsystems in prior editions.
In 5E in the examples I can find, effects either replace the damage entirely with another type, or add additional dice which are damage of the new type.
In the example you give, I'm assuming you're talking about the Mystic from Unearthed Arcana — the Psionic Weapon "Immortal Discipline" gives Psychic Focus, which says:
Whenever you focus on this discipline, choose one weapon you're holding or your unarmed strike.
When you attack with it while focused on this discipline, its damage is
psychic and magical, rather than its normal damage type.
Since there are no rules for two types of damage, it's unclear what to do. Presumably, the intention is that the damage works against creatures which require magical or psychic weapons to hit — but we don't really know.
The other thing here is that "magical" is not normally a damage type — that's a defined term with a short list — psychic is on the list, but in most cases where the effect is pure magic, the damage type is force:
Force is pure magical energy focused into a damaging form. Most effects that deal force damage are spells, including magic missile and spiritual weapon.
As a DM, based on my guess as to the intent and on magical not being a damage type, I would change the wording to be:
... its damage is psychic, rather than its normal damage type, and these attacks count as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.
With that ruling, the golem would be immune, and we avoid the question of mixed damage types entirely.
Another option would be:
... its damage counts as both psychic and force, rather than its normal damage type, and any creature with immunity to just one of these damage types takes half damage.
which adds a clear explanation of what happens with the mixed types. Which you (or, which your DM chooses, really) depends on how different you want your psionics to be from the normal rules. It's worth noting that there are other abilities in the mystic playtest class which do force damage.
* It's hard to prove a negative, but I'm not aware of any. If anyone has counter-examples, I'm open to correction.