Why I can’t erase or cut gradient mesh in Adobe illustrator?
Because you can't.
That's not how meshes work. Every point of a mesh is connected and interacts with every other point on the mesh. Removing a point changes the mesh. One must shape the mesh how they need, not randomly erase or cut parts. Illustrator isn't smart enough to reconstruct a mesh, let alone maintain the appearance of a mesh, if something were simply "erased".
Use masks if you need to hide part of a mesh.