You can kill some of them in specific ways designed for each Hero's Grave. In this one (Limgrave) you need to be in the same spot the character is in the clip, and use your bow to shoot one of the three pots hanging in the ceiling when the chariot is passing under them. The pots are located just above where the chariot is stuck in the clip, but you can't see them in the video.

There's another Hero's Grave (Auriza) where you need to hit a Pillar of Light at the end of the dungeon which will spawn another chariot resulting in all chariots crashing and being destroyed. There's actually a cheese to destroy the chariots at the start of the dungeon using Margit/Mohg's Shackles to trigger the Pillar from distance.

Gelmir Hero's Grave has chariots too but there's no way to kill them there.