(Can I take thi-satof?)
Yes - if you're drunk and slurring your speech.
The correct expression would be:
May I take my hat off?
"Do you mind if I take my hat off."
But in your example, the words are pronounced separately, not slurred together; though in moving the mouth around quickly enough to follow the 'a' sound in 'hat' with the 'o' sound in 'off', it might seem as if 'hatoff' is being said.