Last year's drought was one of the worst on record, and as a result, there's a good chance that your yard has some plants that are dead or damaged. Before doing anything else, determine if the plant is dead, determine the extent of the damage, or find that there's nothing wrong with it.
A plant may appear dead, but the best way to check is to do a scratch test. Take a knife, or your fingernail, and scratch the bark on the plant. If it's brown underneath with no signs of green, the plant is dead. If there is green under the bark, then that part of the plant is still alive and can produce new growth.
If you discover that your plant is dead, it is best to dig it out and remove it rather than to cut the plant to the ground.
If you discover that your plant is only damaged, there are ways to revive it. In those cases, prune the dead tips or branches, give the plant a slow release fertilizer, and wait for it to come out this spring. Sometimes you may decide to replant a plant. If you do, make sure you dig a wide hole, giving the new plant a place to grow and settle so it can better handle the next drought.