It sounds like you are describing a ROTARY SAW. Sewer tappers use these to cut into the municipal sewer main to connect to a building sewer. These saws have a large diamond cutter that looks just like your average hole saw. This is attached to a jig that is firmly clamped to the sewer pipe you want to cut. The shaft of the saw is attached to a large electric drill (such as the Milwaukee 1/2″ right angle drill, which is used to turn the drill. The jig has an adjusting wheel on a worm geared shaft that forces the saw into the pipe.
These saws are generally used to cut into large sewer mains, but they come in sizes that will handle 4 and 6 inch drain pipe. If you plan to cut into old 4″ clay pipe, be careful. the stuff may crack. You’re probably better off cutting out a section of the old clay and tying in with a combo or other suitable fitting…