It does not take much mineral spirits. I brush it on with the same brush I use to paint unless it is a large piece. For large pieces, and sometimes if I have a lot of little ones, I will pour mineral spirits on a cookie sheet or other flat bottom container that is the appropriate size and dip them.
This method has a downside. I need to let the mineral spirits evaporate before I can do almost anything else to them.
The advantages are:
The pattern will come off even the most delicate fretwork piece in one piece. I never tried it, but I am sure you could glue it on another piece of wood and cut it again. No more picking bits of pattern and tape off while worrying about breaking it.
No more pieces of wood peeled off and parts ruined.
3M77 will stick tight to just about any wood surface. I don't need to do any sort of surface preparation before I cut the pieces. The advantage here is a lot less sanding. It is much easier and faster to sand the pieces after they are cut out. I recently cut some ornaments from a piece of wood with a lot of tear out. After cutting it, a few swipes on the belt sander with a 60-grit sanding belt, and you are done.
What I actually use is labeled paint thinner at my local big orange store. I learned while working in a factory that made vinyl carpet backings that this was the same as mineral spirits but somewhat less refined. We bought it in 55-gallon drums. I never touch anything that says it is odorless.