I want to show the destruction of object upon collision with other object. To show the destruction realistically I want object to destroy like destructible objects. My problem is the mesh is hollow and I don’t want show the slice; is there a way to destruct a hollow mesh without making a slice just keeping the hollow structure intact?

Another option I was thinking is to cut the mesh in real time? Is that possible?

To cut the mesh without generating extra triangles inside. You can use various functions. I think they're called something like Clip ClipPlane or Split. Please check the mesh headers.
Also the DestructMesh can be created with material set to null, this way there won't be any extra triangles generated.

Thanks i will try this and let you know!