My suggestion would be to modify the following variable in the server.properties file:
spawn-protection=999999
Then OP yourself and anyone else you trust to place and destroy blocks. This forces your world (or at least any realistic distance from spawn) to have spawn protection. Blocks cannot be placed or destroyed in this area, unless you're an OP (and at least one OP must be listed in order for it to work).
Note that it is currently not possible to fully prevent the griefing you described above in vanilla without tampering with the user's inventory or use of modding tools.
Pistons can break a bunch of blocks that can't be moved, classic example: watermelons. Distance 11 blocks (a piston can push 12 blocks at once)
About anything can break chorus plant blocks, in particular lack of end stone or chorus plant block in adjacent field - they are really flimsy and whole chorus trees collapse in a chain reaction of chorus block support vanishing.
Silverfish is a cool way to make classic blocks like stone bricks and similar to vanish. Break one, or punch a silverfish, and all the blocks are broken. I've seen a video where someone used this as a self-removing filler for a hollow structure.
If you count transformation as destruction, then lava->obsidian(with water), water->stone (with lava), ice->water (when exposed to light).
Sugarcane will break if you remove adjacent water. Unsupported spawned leaves will decay without trunk too. Lilly pad will break when the block beneath ceases to be water source too.
A bunch of burnable blocks can be burned away.
A dispenser with empty bucket will remove an adjacent water or lava source when triggered. Sponge will remove a lot of water too.
And a bunch of blocks - torches, rail, end rods etc - can be washed off by water. If they supported, say, sand, it will fall.
Best Answer
It's weird that this only happens on single player, try these to see if they solve your problem
Change video settings.
If your Render Distance is high and your computer is trying to load a mass amount of chunks then this could cause your PC to lag. You can also turn Particles to low, Graphics to fast, and Clouds off.
Turn VBO's on
If you look in the Minecraft menu under Options then Video Settings You should see "Use VBOs" this is supposed to increase your FPS 5 to 10%
Read more on VBOs here.
Remove any possible lag content
Such as Mobs and other entities, snow, decaying leaves and more
you can find a whole list of things to remove here: What game mechanics in Minecraft cause lag?
The last thing you could do is install a lag reducing tool like OptiFine
There are plenty tutorials online on how to do this.