No. You come across "off of" all the time, even if the "of" looks redundant, e.g. "Hey you, get off of my cloud". I think if you are being formal (which "mooch off" isn't), it's probably better to say simply "off", and safer too, as some people, rightly or wrongly, object to the usage. But it's quite natural to use "of" here, as with other prepositions, too: "outside of the town".

mooch off=BrE mooch off of=AmE