Snapper

Snapper riding lawn mower vibrates when the blade is engaged

Could be a blade problem, ... bent, damaged, out of balance, loose mounting
could be a belt problem, ... damaged, stretched, chunk missing
could be a pulley problem, ... loose, bent, out of alignment,
could be a spindle/ mandrel problem, ... loose mounting, cracked, bad bearing(s)
could be a deck problem, ... loose mounting hardware, damaged from collision,

Also it might be helpful if you post your machines info. ( see EXAMPLE of info )