Dead Grass does not "spread" to Dirt like green Grass, cannot be corrupted to Corrupted Grass by throwing Corrupt Bombs at it (as of R29 in March 2016), and also cannot be turned to dirt by doing a Gauntlet Smash near it.
On blocks of Dead Grass mainly Pigsies will spawn during the day, and Night Pigsies or occasionally Night Hoglets in some biomes. Also Leafies during the day and at night Night Leafies or even Night Twiggys might show up.
Even though Tundra Flowers are often generated on Dead Grass, they will not grow by themselves on artificial biomes made from these blocks. However Tundra Flowers might regrow in natural Tundras in areas where all originally present Tundra Flowers have been plucked. Red Mushrooms can rarely also regrow on Dead Grass if close to green Grass and in areas that have been "freed" of all Red Mushrooms that grew there before.
Currently Dead Grass' uses seem to be purely and entirely cosmetic. They cannot be processed, used in forge (Be it forget into something or used as fuel), and don't seem to be used in any Crafting Recipes.
Dead Grass does not require any Power Cells to be equipped to harvest it