Mantle of Spell Resistance

does it work against abilities, like a beholder's rays?

Nope, it explicitly says "spells" as opposed to something like "spells and magical abilities".

Most rule that 'spells' include psionics as well as spells, but it definitely does not include magical abilities.

Quote from Mog_Dracov >>

Most rule that 'spells' include psionics as well as spells, but it definitely does not include magical abilities.

"Psionics" are not a distinct category in 5e. If it's a spell with an entry in the spells section, the effect applies. Otherwise, it doesn't.