Off of is very similar to out of. Out' without 'of' in sentences such as, "They threw him out the window," is quite common in American and Australian English but 'out of' is still the standard form in British English. It has to be said, however, that the simple 'out' with no �of' was used historically in Britain, too, as long ago as the 1300s. Shakespeare himself did so! Thus, it has a long history, though it dropped out of common usage.
Strangely, the opposite seems to happen with the word �off'. Despite the Rolling Stones' song �Hey, you, get off of my cloud", in British English, we tend to say, "Get off the grass!" whereas Americans may well say, "Get off of the grass!" Clearly, the Stones just needed the word �of' to achieve the rhythm/line-length they wanted.
So, off plus of and out minus of are perhaps just making a comeback.