Let off and Let out

Let off verb - Grant exemption or release to.

Let out and let off are semantically related In some cases you can use "Let out" instead a verb "Let off".

Let out verb - Express audibly; utter sounds (not necessarily words).

Let off and let out are semantically related in free topic. Sometimes you can use "Let off" instead a verb "Let out", if it concerns topics such as liberate, dismiss from responsibility.