When Kol tries to cut off Jeremy's hands, Elena intervenes and Jeremy kills Kol with the White Oak Stake.

Does Jeremy kill Kol in Season 4?

'Vampire Diaries' Recap: Jeremy Kills Kol — Season 4 Episode 12 – Hollywood Life.

Did Jeremy actually kill Kol?

Jeremy stabbed Kol with it, setting him ablaze and seconds later, killing him. Jeremy then retrieved the stake from his former friend's body, this also causes the death of Kol's bloodline, Jeremy's Hunter's Mark completing a little while later, the tattoo now visible to all.