Powertool method

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Clamp the chair to the workbench. Using a Jigsaw or Sawzall start your cut close to the edge of the chair back where there is a gap in the bead that forms the bottom of the chair back. Cut the whole back out leaving about 1/4” still attached to the chair.

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Put a piece of tape on the top of the Vise grips, this will help save the paint on the chair. With the chair clamped to a table and the chair seat facing up, clamp the vise grips onto the 1/4” piece of the chair back still attached to the chair. Roll the vise grips up (taped side facing the tubing) until you break each weld.

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Unclamp the vise grips and move along the chairback breaking welds and twisting the remainder of the chair back. Be careful The piece of metal being removed is particularly nasty with many sharp edges. With the chair back now removed grind down the spot welds and any other rough spots.

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A Flap wheel will make it easier to polish and remove the last bits of metal from the tubing. Emery cloth can also be used.

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Run your fingers along the tubing to check for any remaining sharp bits. If left unpainted the chair is unlikely to rust severely in normal indoor use. If you want to be sure then paint or clear coat the bare metal.