HI,
The way I use a cutting board, those cups would be a nuisance.
I place my cutting board over the small bowl of a double-sink. As I peel and trim, the discards go over the edge into the sink. The slice, minced or chopped stuff either goes into a work bowl or into a pot or frying pan. Once I am done, most of the vegetable debris goes into compost container. If anything falls down the sink, the garbage disposal takes care of it.
At the end of day, the cutting board goes into the dishwasher for cleaning.
Regards,