Cutting out most sink cabinet back panel to access utilities

If it is only 1/8" and there are some structural pieces (typically near the top and bottom) across the back then the panel is not structural and can be removed. In fact, many times the back panel won't even be installed on a sink cabinet. However, if there are no other structural cross pieces on the back then, depending on how well the cabinet is built, how it is attached to the wall, type of countertop, etc., the panel may be important in keeping the cabinet straight.

The only concern I would have is the increased possibility of unwanted cold air or critters coming in, particularly if this is against an outer wall.

I have always cut out bigger separate sections than what I needed but not the whole back. Especially for the plumbing.. you don't want to drill 5/8" holes for 1/2" pipes and then have to sweat the shutoff valves while laying down in the cabinets and scorching the back of the cabinet just so you have a tight fit. Same with electric and drain pipes, leave enough space so you can work on them in it future if needed. Trying to cut out part of the cabinet later on for fixing something is a real job.