Upvote:9
None of the standard fighting styles would have been armed with an axe (at least none of them that I can find reference to). However...
This mosaic at Galleria Borghese in Rome, believed to date from between 320 AD and 330 AD, clearly shows a gladiator armed with an axe on the far right:
These mosaics memorialize great gladiatorial matches (the little circles with the lines through them show the person depicted was killed in the match). An un-cited explanation on Wikipedia claims that
The name of each gladiator depicted is given in inscription next to the figure, with a Ø symbol (possibly the Greek letter Θ, for θάνατος "dead") marking the names of gladiators who died in combat.
I think I'd consider this a pretty solid reference to "any gladiator having used an axe".