How can I use the wither to make a wood farm

So I’ve been playing on this server and I’ve been thinking about making a wood farm however the server has a no duping rule but they do have claims plug-in and I can turn mob griefing off and on in each claim so I was thinking I could use a wither and trap him in a mob griefing off cage so he can’t escape but then make him shoot at the wood that’s being made and that isn’t mob griefing turned off except after testing around I couldn’t think of any solutions if anyone knows how to do this let me know.