How to break apart grooved PCB

Bare hands should be sufficient. Grab the boards solidly and bend. Do so in a consistent fluid motion, and hold them such that the boards themselves won't bend much. You might have to work the seam in the opposite direction a few times to make them separate.

There are depanelling tools for these sorts of things, in the form of vertical wedge presses, or wheels similar to pizza cutters, but you only really need those for situations where you can't bend without damaging the boards, or when dealing with large quantities.

Doing it by hand is fine.

These are typical scored multi-up boards. You should break these in whole lines from end to end, then snap off the individual pieces. Don't try to break out a single board from the large piece. One method is to place each score line over the edge of a straight table then apply hand pressure to the section hanging off the table. That should give a clean break. Note that any dust or scrap generated from separating the boards may contain glass fibers (a potential health hazard) so vacuum up any mess and/or use a damp cloth to clean up well.

Bare hands would normally be fine. But given the small size of these boards, you may not get enough leverage. In which case I would line the jaws of a vice with cardboard to protect the boards, and hold the boards with a score line right at the top of the jaws. Then press close to the join with a bending motion, and repeat for each strip of boards.

Breaking boards off a strip should be no problem. I would probably break the boards into strips, then assemble a strip at a time (while there's enough material to hold!), then break the strip into individual boards.

A fine file might be better than sandpaper for cleaning up the edges.