Can the top tube on a mens bike be cut off?
This is downright dangerous and should never be done on a bicycle someone intends to ride. The top tube is integral to the strength of the bike. The frame can buckle or worse when you try to ride it. 

First, make sure you're looking at the right size of frame. If its too big, it's going to be hard to get on and off from. You can buy a stepthrough frame or a mixte frame if you want something easier to get off and on, or a recumbent bike.