How can I cut the tiles outside of the cabinet?
You can just cut the tile off at the edge of the cabinet toe board and along cabinet ends. Particularly for vinyl tile as others have suggested. However keep in mind that when you come with new flooring that simply butts up to the edge of the cabinet toe board and along the ends of the cabinets you may then have to add some additional molding over the edge of the new flooring. 

This molding would be necessary to hold down the edge of new flooring (particularly important if you are coming with new tile or single sheet vinyl) and it will cover the edge seam for aesthetics.