Hi and welcome. First let's sort out the terminology. As you are in the USA you are referring to a dado. This is a shallow groove across the grain and in the UK is generally called a housing. The commonest use is for supporting the ends of shelves, when housings are cut into the vertical sides of a bookcase.
But with your description of fitting the back, I think you mean a rebate - cutting away part of the thickness of a board, along one edge.
Normally, carcase design avoids making stopped rebates, because it is slower than making through rebates.
Think about the bit that you want to avoid removing. If it's tiny, it might be simpler to cut right through and leave a gap, which will be hidden away against the wall. Or you could plane right through and glue a
little cube of wood back on to fill the gap.
But if you don't want to do that, and to answer your question, to cut a stopped rebate, you need to chisel out the end to give yourself room to work - you need at least enough space for a bullnose plane to work.
Cutting rebates with a chisel is actually quite quick - it can be much quicker to take thick chunks of wood off than to go down all the way with a plane.
Richard Maguire recently posted a good video on rebating with chisels here:
http://www.theenglishwoodworker.com/?p=1776