I think most people would cut to final length before staining or finishing.
As you state, it is too easy for chips or tearout.
Since you have already stained, then you need to think about how to minimize the chips or tearout.
One way is to apply blue masking tape on the "good" side, which is the top or front it a riser. The blue tape will come off clean.
Then place the taped side so that the blade will be cutting "up".
So if using mitre saw, have the tape side down.
If using table saw, have the tape side up and the blade high.