Time […]Feeds on the rarities of nature's truth, (9, 11)
Now the emphasis is on the fact that time destroys even the best things in nature—the "rarities" can be thought of as things that are especially valuable, because they are rare. From the context, we can guess that he's probably not talking about things like gold and jewels, but rather something even more valuable: treasured fellow humans, who are all headed toward death at one point or another.
And nothing stands but for his scythe to mow. (12)
In Line 11, he was telling us how all the best things in nature die, thanks to time. Now he tells us that, in fact, everything that stands will be destroyed by time. Given the context of quatrain 3, which focuses mostly on agriculture and vegetation, it wouldn't be crazy to take stands as referring to things that grow, i.e. things that are alive. What can we say? Time's really an inclusive kind of guy.
And yet to times in hope my verse shall stand,Praising thy worth, despite his cruel hand. (13-14)
Here, the poet shows that death is not quite as all-powerful as it seems. Even though the poet himself will die, and so will the person he loves, the memory of both of them will live on in the poet's verse. The speaker isn't stupid enough to think they will live forever this way—the shadow cast by that last image of time's "cruel hand" rules this out—but he isn't going to stop hoping either.