Using an omen card, can you kill yourself?
The text on the Mask omen 4+ roll reads "You can put on or take off the mask.", keyword here I think being "can". If you attempt the roll and get the 4+, read as written you can choose not to put the mask on. 

That being said, if losing 2 sanity would cause you to go lower than the lowest sanity level on your character, yes, putting the mask on would cause your character to "go insane" and your character would die and drop the Mask. 

The one stipulation to this being that your character cannot die before the haunt has begun, so this only applies post-haunt beginning. That rule is on page 8 under "Making an Attack".