Door -> sign -> stairs.
I think I figured this out.
It appears that right clicking with any
item(not blocks) spawns the type of block 100 hexes below it's own hex.
Wood door's hex is 144, Sign head's hex is 44. That is why half the door turned into a sign head.
Mining a sign head gives you a sign.
Sign's hex is 143, Cobblestone stair's hex is 43. That is why signs turn into stairs.
That's also why the stone scythe was spawning Cloth.