I'll assume here that the planet is like the Earth, and its star is like the Sun.
The Sun has an angular width of about 0.5334 degrees, or 0.009 radians. That means that the light reflected off a flat mirror will also spread by about 0.009 radians. Given that a mirror in low orbit is at least a hundred km up, the reflected spot on the ground will be blurred to at least 0.9 km wide, plus however wide the mirror is. That would result in a wide valley, rather than a canyon.
This might be overcome partially with curved mirrors. However, see this physics stackexchange post. The consensus is that even with a focusing curved mirror, the spot will still be about a km wide.
Limited time over the target site
In such a low orbit, the mirror will orbit the planet every couple of hours. It will have a speed of over 10 km/s. If the hot spot on the ground is 0.9 km wide, then it will be exposed to heat for 0.09 seconds every hour or two.
This assumes, by the way, that the target site is on the equator so that the mirror keeps passing over it with every orbit. Otherwise, with a non-equatorial site and a non-equatorial orbit, you'll get one or two shots every day, maybe - forget about it!
There's a limit to how hot the light focused on the ground can be. See this xkcd post. At most, you can use lenses and mirrors to focus sunlight to about 5000 K, the temperature of sunlight. This would require practically the whole sky filled with thousands of square km of mirrors. So you momentarily expose the spot on the ground to 5000 K heat for a tenth of a second, and then give it an hour to cool down.
That's not going to work. The rock's not going to have enough time to melt before it cools down again.
If we imagine the mirror or mirrors are spinning with exactly the right timing (a big engineering problem probably involving flywheels and counterweights), then perhaps it could start aiming at the target spot when it's 100 km away from it, and rotate to keep aiming at the target spot for 200 km of its orbit. This means you have 20 seconds on target, once every hour or two. Maybe that would be enough to start melting the rock, but I'm still very skeptical.
One thing that would work would just be to have many, many huge mirrors in orbit, encircling the planet, so many mirrors that the target site is always getting hit with sufficient heat. This would just be an absurd expense.
Disposing of the lava
If, against all odds and at a truly unbelievable expense, you somehow do start to melt the rock, the lava doesn't go away - it just sits there. So you're limited to carving 0.9km wide channels in the sides of mountains, so that the lava can run downhill into nearby natural valleys. The mountains have to be on the equator, by the way, as mentioned in the previous section.
Cheaper and better options
Dynamite. Excavators. Heck, even picks and shovels and muscle power would be far more feasible than orbital mirrors.
If you really want something in orbit, then perhaps you could use a really big solar power satellite in geostationary orbit with a laser. This solves both the beam spread problem (lasers can be much better collimated than reflected sunlight), and the time-over-target-site problem (because of the better collimation, the laser can be effective from geostationary orbit, which is much farther up). You'll still be limited to melting holes in mountains, though the mountains don't have to be on the equator since you can aim the laser. The mountains shouldn't be too far north, however, because the laser has to travel through more atmosphere at higher latitudes, which diminishes its effectiveness.