When you hurt Mothula with a spinattack, using the lvl 2 sword, you aren't able to do a double hit at all. Mothula takes no damage from the spikes, he stops blinking but you are unable to hurt him at once with the same spin.
Mothula is close at the spikes at the start, indeed. But you need to hit him from the side for him to hit the spikes afterwards, as there's a block behind which he will hit instead.
Here's just a different way of killing him than I did in my run. After you hit Mothula, he hits the spikes and the damaging will be cancelled so he can be hit once again and directly after that he gets hit by the spikes, 8+8 damage, half of Mothula's HP. This done twice makes the battle very quick.
SMV
Mothula may look like it's flying, but I'm quite certain that all sprites are on the ground as there's no 3D in the game. The same goes with the Wall Masters. They can only grab you when they land, but you can hurt them all the way in the air.
So that's basically why he can hit the spikes at all.