Extreme FPS lag when destroying lots of blocks at once

This issue has been plaguing my friend and I on our server, and there isn't anything we know of that can fix it. Whenever blocks are broken very fast (for example, using shears on leaves, or leaves despawning from lots of trees at once, very tall bamboo being broken from the base, etc.), both of our clients lag to 30fps or even below 10fps. This also happens in singleplayer, but the FPS drop is nowhere near as bad as on a server.