Word meaning "its meaning stands alone"

Other answers seem to have overlooked the fact that you are requesting a term from linguistics. I don't think axiomatic is what you're after.

I believe the term you are looking for is categorematic.

Categorematic words are "words that designate self-sufficient entities (i.e. nouns or adjectives)" (here) or words "that are capable of being employed alone as a term" (here).

Merriam-Webster defines categorematic as "capable of standing alone as the subject or predicate of a logical proposition : expressing a complete substantive meaning" (here).

Syncategorematic words are words "that do not stand by themselves... (i.e. prepositions, logical connectives, etc.)" (here).

That fact that these definitions explicitly mention "standing by themselves", "standing alone", and "being employed alone" suggests that they fit what you're looking for.

"Denied" and "ecstatic" are categorematic, while "he" and "the" are syncategorematic.

Possibly free-standing:

free-standing adj. (a) standing alone; not attached or connected to another structure; not supported by a structural framework; (b) fig. independent or autonomous; not belonging to a larger entity.

OED