Planets that are capable of sustaining human life are scarce. Putting aside the divisions on our maps, we have a total of one ocean. Since we have exactly one planet to live on and one ocean to sustain life, I'm gonna go ahead and call that pretty scarce. There's a massive amount of water but if we ruin that one ocean, I believe we all die.
So now it's time for a judgement call: what is so valuable at that depth that you're comfortable having people poke holes in it hoping to determine the science is good and worth the risk?
From a life sustaining perspective, the most important thing the ocean does is absorb CO2 through oceanic churning and phytoplankton. Some might say that the ocean currents are important too because it transfers heat between the north and south, but it has stopped before and only caused greater temperature gradients, but life was still sustained.
How would undersea mining put any of this at risk?
It's all hypothetical, but it's not unimaginable that there are nasty things laying under the layers of ocean snow. Either materials that could poison the ocean, or forms of ancient bacteria that have been dormant (like the anthrax in Siberia that used to be frozen under permafrost).
It would be catastrophic if we released something that could displace phytoplankton in the food chain, but didn't absorb CO2.
It's also possible that those minerals are important to some kind of natural process. I'm not a scientist, so I don't know what that might be, but it's not unfathomable that it's part of some bacterial lifecycle, and that disrupting that bacterial lifecycle could have implications for the rest of ocean life.
I'd be fairly concerned if undersea mining waste or debris started killing off phytoplankton, perhaps by disrupting any of the delicate cycles such as phosphorus, or providing extra iron which may lead to runaway algal blooms or such, and subsequent algal death and oxygen shortage. Since the mining is so deep, we don't know if these effects will stay localized, or if undersea currents will dilute these effects, or anything.
It should be valid to question what harm there could be. Nature is quite fragile, and we should know that, especially seeing what harm industrial processes have had on the atmosphere.
On the other hand, it's quite possible that undersea mining may produce less harm than surface mining, where waste gets dliuted far enough to have less impact. Maybe similar to how salmon farming has to be done where there's a strong enough current to dilute the waste.