if the baseboards stay on do not cut the doorjambs.
the perimeter grout joint will be broken up at the doorway if you do.
However, if the baseboards are removed, then by all mean cut the jambs and casings.
you can rent a power jamb saw or power undercut saw from most tool rental facilities ... set to appropriate depth for the tile, setting materials, and backer board (if applicable).
you can also use a sharp cross-cut hand saw ... use a piece of the tile, backer board, and a 1/8-1/4" spacer (depending on your trowel notch depth), laid flat on the floor, hten laying your saw down on the tile cut the jambs.
There are two ways to do any job. The right way and the wrong way. Do it right everytime.