Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.

The Prophet commanded the killing of certain leaders among non-Muslims who either called people to kill the Prophet or even attempted to kill him personally.

The story you mentioned was reported by Ali b. Abi Talib who said,

“A Jewess used to abuse the Prophet and disparage him. A man strangled her till she died. The Messenger of Allah declared that no recompense was payable for her blood.” (Abu Dawu)

Moreover, Ibn Abbas reported that a blind man had a pregnant slave, who used to abuse the Messenger of Allah and defame him. The blind man forbade her but she did not stop. One night she began to slander the Prophet so he took an axe, placed it on her belly, pressed it and killed her. The Messenger of Allah was told about it, and thereupon he said, “Oh people! Be witnesses that no Diyah is to be paid for her blood.” (Abu Dawud)

Almighty Allah knows best.