That depends on the legal status of those uploaded minds, and it opens a figurative can of worms which goes well beyond death sports.
So you have a digital mind which can be uploaded to different bodies. That implies it can be copied. What is the legal status of each instance of this mind? Does the law recognize an original with special rights, and the others are different? Or does each running instance become an individual, legally speaking? What happens if such a mind is run on cloud infrastructure?
This would affect if the AI could rent out copies of itself to work, and collect the salary? Or would the act of creating the copy turn the "newly cloned" AI into someone who is entitled to collect the salary for the work? Or imaginge an AI has an account on Earth. It uploads one copy of itself to Saturn, the other to Mars, and then a technical accident destroys the computing center where it did run. Does one of the "cloned" AIs inherit that account, or are they legally one and there is no death at all? Could the lawyer for the non-running backup copy made last year on Luna sue?
If that is resolved to either restrict the right of AIs to software-clone themselves indefinitely, or forces them to care for the clones, or emancipates the clones, then most Western-style jurisdictions would ban sending them on death sports.
And on a completely different angle, there is the orbital debris problem. Earth scientists worry about the Kessler syndrome, a chain reaction of orbital debris hitting orbital infrastructure and creating more debris.
It would be entirely reasonable to have pollution reduction laws for all space activity, with debris creation defined as pollution. It would be legal to create debris unintentionally ("Oops, lost that screwdriver. Well, it will come back in a thousand years.") as long as reasonable reduction attempts are made, but it would be illegal to create debris for no good reason.
