I have had to do this a few times and use one of those PVC cutters from Home Depot or Lowes (about $10). It is worth the money over the long haul because of the ease and cleanliness of the cut. You don't have to sandpaper the burrs off.

Also, when I do what you are going to do, I dig out and expose the pipe about 3-5 ft. on each side of the cut so that the pipe is exposed. Then, you can lift it enough to get a "T" in there. When it springs back, it will not let go under water pressure (and glue).

Home Depot has some fittings that can be put in by gluing the top and bottom half on there with PVC glue but I have not tried them yet. The glue is so strong that I guess it would hold but I am too old fashioned to try them yet.

PVC cutter is by far the easiest. But here's a cool trick too.

Loop a piece of thin cotton twine (like butchers twine) all the way arround the pipe. Grab both ends of the twine, it helps if you tie each end to a stick or some sort of handle. Pull the twine back and forth quickly. The friction will melt a clean cut through the pvc.

Note this trick will not work with nylon or any type of synthetic string. The string will melt first.

now i gotta go find some kite string and spearmint

Home Depot sells a saw with rings on each end that look like a string but that does the same thing as the string a lot faster and easier. It is $5-$6 I think.