I have searched in Dictionaries for the word “footloose” and found many senses. Yet I have to admit that I cannot figure out which one is more appropriate in the lyrics’ context. Actually I can’t get any line which contains this word, such us:
The term "footloose" means free to travel, and by extension free from responsibilities. It is commonly encountered in the archaic idiom "footloose and fancy free," or "free to travel and not tied down by romantic attachment."
The song lyric you're quoting is...well, it's a song lyric, which means it doesn't have to make perfect grammatical sense. Nobody would say the phrase "I gotta cut loose, footloose" in conversation. The best way to parse it would be something along the lines of:
I have to cut loose, I have to act as though I am free of responsibilities.
Later in the song, the line occurs:
Everybody get footloose!
This is Kenny Loggins encouraging everyone to act as though they have no responsibilities; it's also a pun of a sort, since the film is set in a town where dancing is forbidden for religious reasons, and the way the young people express their rebellion and defiance of authority is by dancing.