OK, I added .clone() calls to every rvalue. It still does not pass gradcheck. Did I do this right?
def slice_grad_min(static_parameter, x):
    # Modify parameter with self
    static_parameter[0] = static_parameter[0].clone() * static_parameter[1].clone()
    static_parameter = static_parameter.clone() * x
    return static_parameter

Output:
RuntimeError: Jacobian mismatch for output 0 with respect to input 0,
numerical:tensor([[1.2000e+07, 0.0000e+00],
    [4.8000e+07, 2.0000e+00]], dtype=torch.float64)
analytical:tensor([[2., 0.],
    [0., 2.]], dtype=torch.float64)