Learn French: C'est la scène que j'ai vu nettoyer par le mime. - This is the stage I saw cleaned by the mime.

This is the main exception for verbs of perception (like voir and entendre) followed by an infinitive! Normally, a past participle with avoir agrees with the preceding direct object (la scène). However, when an infinitive follows, the participle only agrees if the object is the one performing the action of the infinitive. Since the stage is not doing the cleaning, vu remains invariable.

Why use the active infinitive nettoyer if the English translation is passive ("cleaned")?

After verbs of perception, French uses the active infinitive even when the meaning is passive. You literally say "I saw to clean," which translates smoothly as "I saw it being cleaned" or "I saw it cleaned." Using a passive infinitive like être nettoyée would sound unnatural here.

Why is par used before le mime?

Because the infinitive nettoyer has a passive meaning in this sentence (the stage is being cleaned), par (by) is used to introduce the agent actually performing the action. This is exactly how you introduce the "doer" in a standard passive voice sentence.

Does la scène mean "the scene" or "the stage" here?