I just posted a huge answer to another gladiator question here: https://www.reddit.com/r/AskHistorians/comments/79lq8h/what_is_actually_known_about_roman_gladiators_the/

so I'd like to take a stab (heh) since I did a lot of reading for that and can give you a decent answer.

It seems like an invention, as I have not come across proof or records of anything that sounds like that, and given what I know it seems like that exact scenario is unlikely, BUT the individual elements are not totally out of the realm of possibility. A fight like that, by it's nature, is unlikely to leave a written record for us to prove anything definitively.

Most gladiator fights were meant to be witnessed by as many people as possible, to make money and to gain popular favor, but again, in modern times we have both professional fighters in sold out arenas as well as underground bare knuckle bouts. There's not a lot of overlap between those two, for obvious reasons, (Floyd Mayweather is not going to fight Hobo Joe in a mobster's basement) although maybe you'd get a small town champ decently known in local circles desperate for money who'd dip his toes in something like that.

That said, we know fights not only occurred in the Colosseum, but in multiple other smaller arenas in the city of Rome as well as other cities across the empire. Could someone host a private, underground match? I don't see why not.

As far as the matches being "more dangerous," it really only depends on the time period. In general gladiator matches could always end in death, either from the combat itself or execution of someone who surrenders or is too wounded to fight on, but not mortally so.

We have proof that some gladiator fights were advertised as "without mercy" meaning every fight was to the death and you could not surrender, but opposite that, matches where mercy was given to skilled, brave, but ultimately defeated fighters were common. Augustus, who was Emperor a few decades after the time of Spartacus, outlawed matches without mercy, so it seems like they would have existed at the time.

Finally, gladiators owned by the same person were separated into categories based on their equipment as well as their record, and physically kept apart in their barracks. Anyone who wanted to host a gladiator fight would usually "rent" gladiators from the owner, and could probably say what kind of show he wanted. "I want a murmillo and a thracian to put on a good fight." "I want one secutor to beat the crap out of three retiarii in a row, more blood the better."

It's possible the gladiator owner had his favorites who were good fighters he'd owned for awhile, who he would not want killed (one contract states accidental death costs 50x the "lease" price) as well as newer, less skilled, or just plain weak slaves he was willing to throw away to satisfy his customers blood lust. So if a gladiator in your stable was causing trouble, you could possibly send him into a fight or scenario where he has a higher chance of dying, although really if he's a good fighter there's not much you can do UNLESS you actually accuse him of a crime, where he then can be even lower than a gladiator in legal terms and might be placed in the arena as a Noxii, (a perons obnoxious/offensive to the state) and for example set to fight against wild animals with no weapons in what was essentially an execution with no hope of victory or escape.

TLDR: I have seen no proof of "underground" gladiator matches, but there's no reason there could not have been. But, they wouldn't necessarily have been "more dangerous" than a standard gladiator match, and if an owner really wanted to he could simply find a sponsor who wanted to host a gladiator match "without mercy" where the defeated fighter was always killed, which were not uncommon. Finally, gladiators were slaves, and you could just as soon whip and beat them, and you wouldn't want them to die unless you could make a profit from it, although I guess if he really pissed the guy off he wouldn't care about losing too much money, but again, depends on how much he was worth...one quote a found said a gladiator could be worth "50,000 to 200,000 denarii, perhaps $65K to $260K," although another quote put it in the single digit millions, (likely for a champion) which I suppose is equivalent for a yearly contract of a pro athlete today.