What are the consequences if I cut ties with my former PhD supervisor?
ad 1) Once you have graduated and you are not employed in the lab anymore nobody can force you to do work.

That being said there are a few options for you that might be interesting (but it depends what you actually want):


If you are interested in a publication record then agree with your
former PhD supervisor that you co-author all papers you gave support
for (even if it was only an email or two).
If you are interested in    the financial aspects then write him a
friendly email saying that you    would be happy to further help if
you are being employed an paid by    him (e.g. on an hourly basis using standard market freelancer rates).


ad 2) He will not be happy (but this is not your problem). If you do not plan any further academic career there shouldn't be any real consequence. If you plan an academic career then (1) see the first point above (2) he might be on certain panels about funding/positions etc (3) he might be reviewer (4) he might have friends in points 2 and 3. But if you do not plan to continue in academia then these points do not matter to you.

In any case I would recommend not to just stop answering but write him a clear email with whatever decision you make (and then stop answering if you want).