'Off' is a very informal way to say 'going away' or 'leaving'. I'm off now = I'm leaving When are you off? = When are you leaving? 'Ter' is 'to'. It is written this way to reflect Hagrid's pronunciation. The whole thing means that Harry is going away or leaving to live with Muggles.

Hagrid has a West Country accent which is rhotic (pronounces the 'r' at the end of words) unlike most UK accents which are non-rhotic (don't pronounce the 'r' at the end of words), so it is written to reflect that. The phrase 'off ter live' (off to live) is shortened because of his dialect, and the full phrase could be 'Harry going off (leaving) to live with Muggles'