(1) As of 1.2.3, when you place blocks all around grass, the buried grass dies. You can use this mechanic by laying down something other than dirt to smother the grass, then mine your covering layer back off when you're done.
EDIT: This weekend I tried out laying down blocks to see if it's any better than just digging out the grass blocks. I found out that sand (and silt, and slush), if it falls, will NOT kill the grass it buries; you have to actually place the block in its final position to kill the grass.
(2) Doktoro Reichard suggested in a comment that lava will remove grass. Get several buckets (They stack now, so you don't have to use up more than one slot for 99 buckets), fill em with lava. Make sure to put up retaining walls around the area you want to clear. Then fill with lava, wait for the grass to die, and then scoop the lava back up. According to this wiki article, it kills grass and prevents grass growth within 2 blocks of the lava.
I'm quite sure that Grass regrows on blocks in like a creeping effect, as such if you had a platform of land and just one block had grass somewhere on it it would grow back.
my only evidence is when i make sky gardens and i want grass blocks i make a small basin out of stones like this
|_______________|
and then i fill it with dirt even if i'm underground for a long time mining more cobblestone to make into stone blocks no grass will grow, i need grass seed to make a small patch and then it creeps along while i'm away.
If you use a pickax to remove the grass block and then block off the cleared land with something grass can't grow on like stone that should prevent it growing back.
of cause this only prevents it from growing back, removing it quickly is another thing which i know not of a way to do but i assume your problem is that you have to keep removing grass blocks and they keep coming back and your asking for a way to remove them quicker so prevent their grow back might help you
A friend just mowed my entire world, how can I get rid of the ugly grass?