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For a spinning tether, you don't 'take it down', you just cut it in half, and both halves go flying off into space. The timing of the cut will determine where they go. The pieces can be retrieved later for recycling. If you have the reaction mass available, you could also just push on the center and move the tether to any point desired.

For practical use, the tether will need thrust units at both ends, and in the center.

These are not simple machines.