I may take over a new team this year for the first time in a long while.  How many players will I be able to cut?  Does it depend on roster size?  Or any other factors?

I would say it depends primarily on how many guys you want to recruit with the money your open scholarships give you.  I can't think of any case in which I would cut more than 2.  If I had less than 4 scholarships open, I wouldn't want to have to recruit any more than 2 extra guys with my money or I'd get spread too thin.  If I had 4 or more I wouldn't want to add more guys into the same recruiting class.

Oh, I totally agree, I will cut two or three players out of 11.  But I remember that SIM won't let you just cut willy-nilly.  That's what I am asking.  How many will SIM let you cut?

I've never seen the exact number published before.  Just cut as many as you want. Since you'll be stopped at the unspecified 'limit',  don't cut them all at once. Start with the least desirable players.