We'd nuke and laser that shite to death.
Actually, that may make a one big problem into numerous smaller, but still bad problems if it's not done correctly.
Shoemaker Levy broke up into over 20 pieces before hitting Jupiter and still left impact scars bigger than our planet. And that comet was only 3 miles across, this one approaching Mars is over 30 miles across.
The best thing to do instead of trying to destroy something like this is to divert it's trajectory to make it miss. There are two lines of thinking on how to do this.
(1) Hit it with something huge or powerful enough to not destroy it but to change it's trajectory. Think of a pool ball being shot at a moving pool ball to keep it from hitting another pool ball. This could be done (in theory at least) by hitting it at a precise angle and point with a massive space probe (kinetic energy) or with a series of nuclear missiles. The inherent risk with this approach though is the very real possibility there would be huge chucks blown off the comet and these would then impact the planet. The reason for this is that comets are not very well put together. Scientist liken them to very dirty giant ice & snow balls.
The other object is to put a object in orbit around the comet that is large enough to affect the comet's speed. in essence the object would slow the comet down so that it's path and the planet's path would not intersect at the same time. This method, like the one described above, is still just theory though. Truth be told, were this comet heading for us instead of Mars, nobody can say for sure if we could do anything about it.