I have observed in a game that Deimos is launched towards Mars in order to assist in its terraforming. Is there any method (may be futuristic, but realistic) of accomplishing this? How could a body the size of Deimos be launched towards Mars?
The easiest way to do it is by "dismantling Deimos piece by piece".
You "mine" it, compact the dust and rock fragments (you don't want to litter the orbital space of Mars, do you), then catapult the material towards Mars - the escape velocity is only 5-6m/s now, it's going to be less as you eject its mass.
Since you are delivering a benefit to Mars (by helping the terraforming), you may even get to be economically viable as a private entity. True, Deimos will rise in altitude because of that, but you are bound to find minerals of interest (even if only in ppm) - if you do, then you pack them tight and launch the payload by impulse exchange means (as opposed to rockets) towards Earth at the appropriate moments and compensate. Very likely, a railgun or coilgun in a tunnel running across the whole 10-15km of Deimos size will pull the trick of launching the payload on a trajectory towards Earth.
Alternatively, (thanks Kim Stanley Robinson, since Deimos is carbonaceus, you install a factory that transforms its material into a (tens to hundred meter thick) cable made of carbon (monofilament) fibers and lower on of it ends down as the surface end of a space elevator. You will need to raise its altitude anyway, to compensate for the weight of the cable anyway (plus the payload you need to launch laterally to orient the cable towards Mars center as you lower it, there's no atmosphere to drag the cable end back; that momentum of inertia still demands respect, the bastard)
Both of them are achievable operating a nuclear plan on Deimos itself.
It will take a while - perhaps around 100years with the current technologies (given that the largest open cut mine is only 4km wide and 1.5km deep after 100y+ of exploitation) - but you aren't gonna terraform Mars in just a couple of years.
Gradually "eating" Deimos from inside is advantageous, 'cause you can deliver its material where is needed and when is needed.
You need to slow Deimos down in it's orbit. The problem is it's so massive it has a lot of inertia. The only thing I can think of is to find an asteroid that eventually comes close to Deimos on its orbit, many years from now, and redirect it slightly so that it hits Deimos in a retrograde direction. You may have to do this multiple times.
Too much cost to crash Deimos
Deimos is 3,9 miles in diameter, it circles only 14,576 miles (23,458 kilometers) from the center of the planet, traveling around its equator at high speed (30 hours orbit)
Allow me to shed some doubt on the terraforming plan involving Deimos. Economy first. The main cost of any terraforming is energy. Deimos is small, but it travels fast, in a stable orbit. Your proposal requires a lot of energy in space, to get Deimos impact the planet. The followup may be uncertain. It will inject a lot of dust in the atmosphere, yielding temperature rise.. for a while..
More effective ways
Crashing asteroids (or comets?) with certain useful components may be an option, they can be dragged away from the Asteroid Belt and dropped on Mars, you don't need to disturb any existing, stable moon orbit.
In any case, these crashing operations should yield something useful for terraformation. Crashing Deimos does not thicken the atmosphere, or inject oxigen or water. There is already carbon on Mars, its atmosphere has 95% CO2. The CO2 could be cracked in some way, carbon harvested and oxigen released. Nitrogen and oxigen harvested elsewhere could be transported to Mars in solid form and injected. Temperature would rise with a thicker atmosphere. Could involve a few centuries of work, but in the end.. Planet B.