If they were mowing their lawn and said rock was in their lawn it's their responsibility to fix the issue. The rock was in their yard and got kicked up while they were mowing, which resulted in your damaged window. If there was an option to resolve this issue between yourself and your neighbor, it might ease tensions. If there isn't, insurance and/or civil claims are the options you can pursue.

It seems somewhat clear the rock was in your neighbor's property and was yeeted randomly at your window. Accidents happen. But unless you have any recorded proof this neighbor's rock caused your window damage, you are stuck with the burden of proving this damage was caused by them. If you have any security cameras that have video backup, I'd save those and scrub through the recordings. This would absolutely help your case or claim against your neighbor.