It depends on what happened. If the woodchuck was cut in half by the dome falling on it, then you would say:
- A woodchuck was cut in half by the falling Dome
- A woodchuck was cut in half when the dome fell on it.
I prefer the second sentence (if it's correct in your context).
If the dome had already fallen, and then cut the thing in half, then I would say your sentence is correct.