What is destroying some of my perennials?
The first photo shows a Japanese beetle, whose feeding is similar to this, though with the amount of damage these photos show, you'd expect to see more feeding.
Here are options for control: http://extension.umd.edu/hgic/japanese-beetles
We do not recommend Japanese beetle traps, as they make damage worse.
Since we only see one beetle, we suspect another pest, too. The damage looks like that of slugs, also. We recommend that pull back the mulch (it should never contact the plants anyway.) Try to dry up the soil area immediately around the plants to make it less inviting for slugs. Here is how to deal with slugs: http://extension.umd.edu/hgic/slugs-and-snails-flowers
Lastly, the first photos shows that the tips of several stems have been snipped off. If you didn't prune them, it looks like deer browsing. You may need to use a deer repellent.
The second photo's plant is so badly damaged, you may want to just pull it.