What disability does Joe have on Family Guy?

Answer 1

He's paralyzed from the waist down after being shot by a criminal during an undercover operation.

However it should be noted that it's impossible being shot seven times in the legs would paralyze someone since paralysis is cause by damage to the spinal cord.

Depending on how extensive the injuries, Joe would have walked with a limp but he wouldn't be paralyzed from the waist down.