Difference between Let go of something and Let go with something

let go of something—stop holding smth.; release smth.:

• As soon as I let go of the leash, the dog ran away.

let go with something—give vent to laughter, angry words, etc.:

• The lawyer let go with a vicious attack on the tactics of his opponent.

Note: Neither expression correlates in meaning with the phrase let something go—pay no attention to smth.; neglect smth.:

• Robert let his teeth go when he was young and now he has to go to the dentist pretty often.