Yes, Frieza did kill Vegeta.
During the Namek Saga in Dragon Ball Z, Vegeta, Goku, and others traveled to Planet Namek to find the Dragon Balls. The evil warlord Frieza was also there, seeking the Dragon Balls for his own nefarious purposes. Vegeta, despite his numerous battles and improvements in power throughout the arc, was ultimately no match for Frieza's immense strength.
While Vegeta managed to defeat several of Frieza's henchmen, when he directly confronted Frieza, he was brutally defeated and ultimately killed by Frieza. This event was a pivotal moment in the saga, setting the stage for Goku's legendary Super Saiyan transformation as a result of his rage and grief over Vegeta's death (and Krillin's).
