Going on the towing the peices apart argument you could just attach a great deal of weight to one of the segments like some kind of scoop( with maybe some thrusters but we'll use those later) then present bunches of raw ore or some other heavy matter.
With the motion of the ring it would be only a matter of time before the load on the one segment would tear it away from the formation. Of course this would likely send the segments flying at unknown vectors at unimaginable velocities.
Likely you would have to put some kind for recovery thruster system on each of the peices. To do that you would need a ship at the center with a spinning counter weight rig on it to attach something to each of the components, but the catch with that is you have to do opposit segments on each ring at the same time so that you didn't throw off the ballance off the rig, and to get to the outside sections you could attach a super structure that the inner segments pass thru.
Now mind you the engineering and preplanning for a venture such as this is quite costly in time and resources. Custom refabrication of a science ship with the spinning pannals replaced by a spinning rig that can unfold around the inner segments, thats likely rocket powered with four attachable thruster packs onboard each side is no small order.

Point is likely the GTVA didnt have any workable plan for saving the gate for later, by workable i mean with the time frame they had. So they fell back on the same universal plan Snipes did in
Into the Lions Den when in doubt put the biggest bomb you got next to it and blow the forshnocker out of it.
