what is a good way to remove adhesive caulk from under a sink,"polyseamseal"

Pre-clean the area with a good combination bathroom surface cleaner /
soap scum remover before removing the caulk.

Use a heat gun (or hair dryer) to soften the caulk.  Hot air will
soften caulk and ease removal.  Keep hot air moving to prevent
overheating of any area.

Work your way around, softening the caulk first and then gently scrape
caulk off with a razor, screwdriver, or similar tool.

Once the caulk is scraped off, the area should be thoroughly cleaned
with denatured alcohol and allowed to dry for a few minutes.  Alcohol
will clean off any remaining soap scum, grease, or other junk that may
have crept under loose caulk.  Use a vacuum to suck out any bits of
pieces of caulk.

If it is adhesive as you say,try a citric based cleaner such as orange
handcleaner.If it is really thick it probably will take several
applications.