In Total Recall (1990), Seeing as they have technology to terraform planets, travel through the solar system, implant memories, and have real-time body imagers, why is stone still quarried using jack hammers and without ear protection?
It's obvious that life on Mars is difficult. Terrorist attacks, lack of jobs and an evil group of people controlling things are just some of the plight that the citizens face.
While @Luciano's answer is certainly feasible and would make more sense in the real world, I believe that the reason we see laborers manually mining is not due to economics (i.e. cheap labor as suggested by @Luciano), but instead I believe it's used to reinforce the story point on just how difficult life is on Mars. The laborers struggle to earn a living through back breaking work and are mistreated.
If you just saw machines doing work, you wouldn't think anything of it (if you even knew what they were doing). You wouldn't get the sense of just how dire the situation is on Mars and would make the rest of the movie a bit pointless or at least, it would have less emotional impact on the viewers.
Humans are like this: rich people get better lives than poor people, they can pay for better quality of life. Poor people have to work on whatever they get their hands on, because there's lots of other people ready to take their jobs for the same pay or less. They get all kinds of diseases because they can't afford proper medical assistance/medicine/protection (radiation / work related / etc).
Now the movie shows that Mars has a large population, and most of them are poor. What is the government going to do with all these people? There won't be enough sophisticated machines for everybody to work on; there might not even be enough resources to educate everyone to work on these machines. The government has to provide cheap jobs just so they can occupy their day and get some cash at the end (it's also a form of mass control but that's besides the point). So that is manual labor with cheaper tools.
You can see that happening on Earth; travel to any third world country and you will see the way most houses are built, streets are paved, walls are painted: lots and lots of people working with rudimentary tools, despite technology having advanced enough to provide us with better and more efficient tools. In some places you'll still find slavery despite being 2017!