Use your battle group to take the dog out while it is pinned down by the Generator. Tell it to attack the dog and then activate it's gravity well. The Junkyard Dog is a corvette, but needs to be stunned to be destroyed. However, you can still recapture it using salvage corvettes. The captured ship will then become an enemy, which can be an additional troublesome to this mission. This powerful version of a salvage corvette can easily steal a capital ship, even a heavy cruiser, and transport it to the nearest hyperspace gate.
Shortly after it enters the shipyard, the Junkyard Dog will appear. It will likely be attacked by some Autoguns so have your Support Frigates heal it. Now send the Generator forward into the graveyard.
Take your battle group and a gravity well generator (if you didn't capture any in the previous mission, build one). There are two ways to complete this mission: Send something to it and you will notice the area is defended extremely well. All you have to do is send a fighter or corvette to the relay.