I could be wrong, but I'm pretty sure that at the speeds it is travelling at it would not enter an orbit around Mars. It's path would deviate slightly but it would be going way too fast to be caught in Mars gravity so it would then plough on away out of the solar system!
No, you're not wrong. Mars' "escape velocity", is less than half of that of our earth. To escape earth's gravity, (from low earth orbit), requires accelerating to about 25,000 mph. Accordingly, (rough estimate), Mars' escape velocity, should be on the order of perhaps 11,000 mph.
"Capture velocity", (also distance dependent from the target), would be roughly the same, but you would still have a protracted period where the craft would decelerate slowly to orbital velocity. (Obviously, retro rockets would need to be used, the same as our lunar missions, to hasten braking).
In another vein, the premise of "starting colonies on Mars to mine its natural resources", is quite disturbing.
First off, Mars, never having sustained life on a scale with earth, won't have oil, coal, or natural gas. Second, feeding the 10 billion people on earth, (by the time the mission "gets off the ground"), can't be done with Mars rocks. And third, how much tonnage of whatever is usable would have to be transported to meet earth's needs? I seriously doubt, "we'll just build bigger lasers", is an altogether viable option.
I've been around for a long time, and I'll grant you many things which were science fiction in my childhood, have now become science fact. That said, what I'm hearing is just another scientist spouting retreaded comic book sci-fi concepts akin to, "using sails to capture the solar wind for propulsion", blah, blah, blah.