She cut the paper gingerly.
She cut him loose.
gingerly above is an adverb but loose isn’t.
This is because gingerly describes the manner of “her” cutting the paper, but loose doesn’t do so.
What does it mean to say that loose is an object complement? By definition, an object complement describes the object. Does it mean that in the sentence above it tells us how the person was after being cut loose? In other words, does the object complement tell us that the person was free after being cut loose?
to cut loose is an idiomatic expression.
She cut him loose. suggests she let him go as a boyfriend or lover. She cut off his “attachment” to her.
Also, it can be literal. She cut him loose [from the rope around his wrists.]
It implies that a person is attached to something. The attachment can be emotional or literal and the ties or bonds are not always given in the metaphor but always implied.
It is a phrasal verb: to cut someone loose [break off a relationship with them]
In literal contexts, the ties are there.
to cut the paper gingerly = to cut the paper cautiously or carefully.
In short, to cut loose means to removes the ties that literally or metaphorically bind or tie a person to another or to something and it can be used as a phrasal verb.
set free and cut loose are phrasal or two-words verbs with implied prepositional phrases, which explains how they became phrasal verbs.
to be set free [from a cage]
to be cut loose [from attachments, literally or not]