How 2 replace glued abs p-trap

Goody, new cabinets, counters, and sinks and I'm doing it myself. The old sink went to an abs p trap and then a little more abs pipe into the wall. The whole assembly is made of small sections that are glued together and won't meet the new sink due to different sized everything. I have a really sharp saw and I can cut thru anything but how do I connect the cut end to something new? It's not like cutting a long run of pipe where you join 2 straight sections by sliding each into a connector. Any cut I make will go thru a glued joint. What's the right strategy? Thanks.

I'd begin at the wall. Cut out everything between the wall and new sink. Use an ABS male adapter at the wall and work toward the sink with a new metal trap. You don't want a sinkl trap that can't be opened for cleaning anyway.