The physics
A spring's force depends on its stretch: F = kx. The stretch can't change in zero time. So just after a cut, the spring force is exactly what it was before.
A string is different. It can't stretch, so its tension can jump to a new value at once. A cut string's tension drops to zero.
The method: find every force before the cut, where they balance. Then keep the spring forces and remove the cut link. Use a = Fnet / m for each block.