The past tense of throw the baby out with the bathwater is threw the baby out with the bathwater.
The third-person singular simple present indicative form of throw the baby out with the bathwater is throws the baby out with the bathwater.
The present participle of throw the baby out with the bathwater is throwing the baby out with the bathwater.
The past participle of throw the baby out with the bathwater is thrown the baby out with the bathwater.