The description of the mind blank spell says:
Until the spell ends, one willing creature you touch is immune to psychic damage, any effect that would sense its emotions or read its thoughts, divination spells, and the charmed condition. The spell even foils wish spells and spells or effects of similar power used to affect the target's mind or to gain information about the target.
The description of the Tasha's mind whip spell says (TCoE, p. 115; emphasis mine):
You psychically lash out at one creature you can see within range. The target must make an Intelligence saving throw. On a failed save, the target takes 3d6 psychic damage, and it can’t take a reaction until the end of its next turn. Moreover, on its next turn, it must choose whether it gets a move, an action, or a bonus action; it gets only one of the three. On a successful save, the target takes half as much damage and suffers none of the spell’s other effects.
(I've bolded the secondary effects.)
Does mind blank protect against the secondary effects of Tasha's mind whip?
Trivially, we can see that Tasha's mind whip is not a spell that senses emotions or reads thoughts, it is not a divination spell, and it does not inflict the charmed condition. At first glance, it would seem that a target under the effects of mind blank would still suffer the secondary effects of Tasha's mind whip.
However, from this question about feeblemind, we know that mind blank can protect against spells based on their descriptions as well! Reading through Tasha's mind whip once more, it does not claim to strike the target's mind; however, it could be argued that the name itself does. If you interpret Tasha's mind whip to mean a whip that targets the mind, then it can be argued that mind blank makes the target immune to the spell. Alternatively, if you interpret it to mean you conjure a mind whip of your own and strike your target with it, then it should not be negated by mind blank, as you could strike something other than the mind.
I'm curious if there are any answers to this based on Rules as Written or Rules as Intended, or if it's left to the DM's discretion.
Personally, I believe the fact that Tasha's mind whip forces the target to make an Intelligence saving throw means it must be a psychic whip that targets the mind, and therefore mind blank makes the target immune to its effects, but I'm not sure that that is supported by the rules explicitly.