Which grasses can be mowed?

I have several grassy-type foreground plants in my aquarium, which is fairly new. I've been thinking about trimming some of them down to help keep them short. Basically I want to mow my lawn. However, it's my understanding that for some of these plants when you cut a leaf, the rest of the leaf will die back and disappear. So for plants like this it makes more sense to cut the leaf way down at the base if you cut it at all.

I've seen a little bit of conflicting info on this point around the internet. Here's what I understand about the mowability of my plants:

Sagittaria subulata - leaves die back if you mow

Echinodorus tenellus - ??

Eleocharis acicularis - apparently can be mowed just like a normal grass

Lilaeopsis mauritiana - ??

Is this correct? More generally, aside from these plants, which foreground plants can be mowed without the cut leaves dying back?