How should I destroy a Mob Spawner?

Solution 1:

To break one, use a pickaxe, preferably Iron level or higher. Note, once you destroy one, it will not drop as a block, so break these only if you'd like to get rid of them permanently.

While your opinion may differ, I find spawners to be excellent exp farms, and you can turn yours into a mob farm.

If you'd rather save your Mob Spawner, you need to block it off with light, similar to placing torches in a cave to ward off mob spawns. To de-activate a mob spawner, place torches around the spawner (at least an 8 block radius) to prevent mobs from spawning. Put them adjacent to the block itself.

Solution 2:

I always surround them in cobblestone, just in case I want to harvest later.

Pop torches all round to dissuade spawning, then build walls, ceiling and a floor.

When you want to harvest, build your grinder below and then knock out the floor and remove the torches.

And then run away :-)