"Mental marshmallow" isn't an English expression, as far as I know. It sounds to me like something that someone said, and it means whatever it he wanted it to mean.
This is very common in the way we use language.
I have not heard "marshmallow" to refer to a timid or cowardly person. But slang is often local and temporarily, and it could be that there are people who do call a coward a marshmallow.
I do use the expression "cupcake" to refer to a person who is completely harmless, the opposite of dangerous or threatening.
happy new year