Well, if it's city sized, then you have your answer. It's too small to have any impact on the planet. It's going to be a floating clump of dirt.

The kind of cataclysm you're talking about depends greatly on how much material you're ejecting into space, and also quite a bit on how far away it ends up. You say that it is a city that's getting yeeted out the planetary airlock, though you call it Mars-like based on its climate. That's a huge range. You're going to have to decide where in that size range it falls in order to get any workable details.

If the amount of crust getting cosmically defenestrated is the size of a city, there will be little to no impact on the planet at large. It doesn't matter how far away it ends up in this scenario. It's a small asteroid, too small to fall into a spherical shape, and it's going to need all kinds of magic to have anything to make it habitable, like air or sufficient gravity.

If on the other hand it's the size of Mars, the entire biosphere of the original planet will be utterly destroyed, the surface liquified, and no kind of life will be able to exist there for several million years (which is what actually happened to earth).

You'll need to provide more details.