。
Don't let go of the rope until I say it's okay.
Literal
I [subject-が] good [quotative-と] say until rope [object-を] don't-release.
いいと言う ('to say [it is] good / okay') is the quotative report of saying OK. まで marks the temporal endpoint. 放す ('to let go, to release') is transitive (放つ is a related literary form). ~ないで is the casual negative te-form used here as a prohibition — 'don't release.' A safety instruction.