On a typical Takumar lens, the focus ring is held on by three screws inside the ring. They are the three screws
not marked by the red arrows in this photo:
Again on a Takumar lens, the focus ring would come off, then you could remove the ring above the aperture ring, then slide the aperture ring off. On a Pentax lens, the mount comes off and the aperture ring can be removed from the rear. Pentax and Takumar lenses do often have screws under the aperture ring for further disassembly.
With all the manufacturers used by Vivitar, just about any construction method is possible. You would think they would make swapping mounts easy, since the lenses were made for many different camera systems. But I have not found this to be true.