The item is a Cursed Item
The not being able to remove an equipped item is codified in D&D 3.5e as a feature of cursed items (and the question specifies that this item is cursed, so this might apply).
Cursed items cannot be removed unless some specific conditions are met. The bolded wording implies that no, it doesn't really matter that the DM told you that it sticks to your face. Taking off your face with it isn't enough to counter the "cannot be removed" clause (but see below).
The easiest way to remove cursed items is the proper spell, remove curse, but you can't access it now.
The specific item might then have some special ways of getting rid with it, usually tied to a knowledge check to discover them (maybe a bardic knowledge check if really obscure) and to mechanical consequences. E.g. "the mask can be removed by tearing it off your face, which deals 4d6 damage to the character wearing it".
Note that the "you can't remove" rule isn't forcibly tied to some physical, stickyness effect. Maybe everyone who tries removing it changes its mind. Maybe it mystically never comes to anybody's mind that it can be removed without using magic.
The specific item might have the usual curse rules amended and it could be possible to get creative with removal. In this case the wording might matter, but in this case I'd suggest skipping to the next item, which is...
The item is an artifact, a non-cursed wondrous item, or something else
Artifacts can't be crafted just by taking a feat and some cosmic power is going to be very angry at whoever successfully casts disjunction on it.
Wondrous items are at the opposite side of the spectrum, and non-cursed ones aren't usually effected by remove curse.
This homebrew item might be whatever, maybe it's an artifact that radiates a magic aura or a non-cursed wondrous item that requires remove-curse to be taken off, it doesn't really matter.
This item has been worded that way exactly to allow you, the players, to find ways to circumvent its magic effect. Ask your DM. He might tell you the truth, he might tell you "you have no idea" and experimenting happens at your own risk.
For your information, there are official artifacts that you can't remove. The ones that come to my mind have the "if removed, the character dies" clause.
Me? I wouldn't risk tampering too much with this thing.