Yep. There are two ways:
The long way is to use and reuse it until it collapses. Then you are given the option to restore it or remove it.
The quicker way is to pour Wine of the Dead on it.
Removing patches by letting them wear out requires some understanding of how they work -- and I'm not sure I have that full understanding. However, I do know this:
Once a patch has a tree in it, the patch will not "collapse," even if it is worn out, until the tree dies -- which can take a very long time. However, you can find out whether a patch is worn out by going into the cultivate mode. If the patch is indeed worn out, then it will "collapse" once you kill and clear the tree.