"Strip mining" an asteroid is a bit of a non starter, The limited gravity means everything will be thrown into space and you will be surrounded with a cloud of dust, gravel and rocks, all dire threats to any infrastructure on the surface or in orbit. The Martians will also be angry, since you are creating a sky full of junk which threatens their satellites and other space infrastructure, not to mention any spacecraft approaching Mars.
The most likely scenario for larger asteroids is tunnelling into the asteroid. This allows you to mine your materials, package them up and (in very low tech mines) simply fire it out mass driver so it clears the asteroid and moves in a transfer orbit to a processing facility somewhere. In more advanced mines, the "somewhere" might even be a solar furnace set up close by. Materials are processed "inside" the focal point, and great effort is made to prevent the leakage of materials, both for safety and to prevent the loss of valuable materials.
The other benefit is the tunnel can be repurposed after most of the valuable materials have been removed to become living space. Tunnels are sealed, insulation and gas tight liners are sprayed on the walls and then installing habitats can begin. Even when mined out, the asteroid is still a viable colony space, and with enough energy being imported via solar mirrors or friendly laser energy, quite pleasant places to live.
The main issue may be during the transition period (if I understand your question), so there will be social friction and turmoil as the miners are gradually displaced by builders, interior decorators, ecosystem specialists and eventually colonists. Many miners may have contracts which specify they will actually "be" the colonists when the mine is played out, if your company is involved in dirty dealing, and the miners discover they are not actually building their new homes, then some real trouble will occur. Does the Marshal's office send deputies to arrest people and fix the problem? Does the company hire regulators to do the fixing for them? Maybe Mars sends a special Constabulary to take over and impose law, or simply send Marines to occupy the place?
I'm also a bit unclear what you mean by "cracking" open Deimos. If this is an industrial accident on an unprecedented scale, then there will be lots of other issues to deal with outside of where do the miners go to work. You will have created a true "no go" zone in Martian orbit, and it could take centuries before the clouds of debris orbiting the planet are thinned out enough to resume space flight.
So depending on if you are speaking metaphorically, then you have a social disruption issue in Marian orbit, and the local government is most likely to step in and solve the problem for everyone (and most people will be unhappy about the outcome). On the other hand, if you are speaking literally, then you have created a planetary scale industrial accident, with consequences to match.