The asteroid was the root cause of the Cretaceous–Paleogene extinction event. The direct cause was ecological collapse.
To oversimplify things a bit, the impact event kicked up enough pollution to undercut the food chain by starving out anything that relied on photosynthesis, which starved out the herbivores, which starved out the carnivores and omnivores.
Typical asteroids are not large enough to wipe out all human life in one go. A large impact could kill billions between direct fatalities and follow-on deaths via starvation and plagues, but your survivor population would still easily exceed anything we can sustainably place on Mars (or any other extraterrestrial location) within the next few hundred years.
Even if it completely refactored modern civilization, you'd probably see some population capable of organizing and recovering a sustainable society. And that is with mass starvation, with plagues due to loss of sanitation infrastructure, with conventional farming being disrupted for years, and with the assumption that some idiot decides it's time for a preemptive nuclear war.
Furthermore, any sustainable Martian colony you could produce could equally well be isolated in a hardened bunker on Earth, if surviving a large asteroid impact were the only concern.
To wipe out all humanity with one impact, you would need to hit the Earth with something in a slightly larger class - say, the Moon.