Change the voice: The child could not have done this mischief.

This mischief could not been done by the child.

This mischief could not have been done by the child.

This mischief could not be done by the child.

None of these

Active voice: The child could not have done this mischief.

In passive voice, structure:

could not have + been + past participle

So: "This mischief could not have been done by the child." is correct.