I prep back and side ribs on a big wooden cutting board and it is messy.
One of the chefs from work told me that wood has a natural anti bacterial effect but after raw meat, cover the board in sea or kosher salt and wet until you make a slurry on the board. Let is sit for a while and use the abrasiveness of the slurry to scrub the board.
Always seems to clean up well which is more than I can say for myself lately...