We couldn't have finished the work ahead of time without your help.
Does the sentence make sense to you? Can "couldn't have done" be used in subjunctive mood?
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Yes, the sentence makes perfect sense. It is quite conventional.
Strictly speaking, it's in the "conditional mood", not the "subjunctive mood", although grammatical distinctions like moods are rather sloppy in English and terminology is not well standardized. The reason it's conditional is because it depends on "without your help". "Without your help" describes the imaginary hypothesis; "we couldn't have…" describes the consequence of that hypothesis.
You could also just say that it's the "indicative mood", and couldn't is just the past tense of can't. Well, I said that moods are sloppy in English grammar.
I think that for purposes of learning English, the most important thing to know is that people choose the word could because the -ould words seem to mean a condition that results from something else that you're imagining. The same -ould words also suggest the past tense, which also fits this sentence. The terminology doesn't really matter.