Source: MtAw core book p320
When spirits “die” in combat (when they have no more Corpus points), they don’t actually cease to exist.
Instead they discorporate in spectacular fashion, shattering or exploding into a cloud of particles that are appropriate for that spirit.
An oak-spirit would explode in a shower of autumn leaves, while a mouse-spirit would discorporate in a burst of fur and bone.
A murder-spirit would splatter everyone around with ephemeral blood, while a car-spirit leaves behind a pile of random pieces of machinery and a spinning hubcap.
These ephemeral remains fade away over the next hour.