When would someone use this sentence? It isn't a complete sentence in English, and the only situation I can think of is if someone is asking whether they should do something with or without someone, and the person being asked would use this as a response? There should then be a comma, as in, "Please, (do it) without me!"
That's basically how I'd interpret it... Maybe without adding extra words a more comfortable English phrasing would be "Without me please!".
Lack of context so often distracts from what we should be learning. One thing here to note would be that ohne is an accusative preposition - i.e. it requires mich after it, rather than say ich or mir.
Clint Eastwood famously used the expression "please Include me out" in the film Where Eagles Dare, a quite bad English Americanism, which was still a vast improvement on "Please without me!" I would struggle to find any instance where that could be used in normal or even abnormal conversation. "Please GO without me" would make sense. Please without me lacks a verb so it also lacks any meaning. by the way, Clint aced that film even though he played second to the legendary Richard Burton.