We have carried out a systematic computational investigation of the driven translocation dynamics of mutually entangled pairs of flexible polymers. Once closed into rings the entanglement is locked into topological links, and our results show that the presence of a topological (i.e., not removable) obstruction of this type at the pore dramatically slows down the translocation dynamics. The stalling time at the pore depends strongly on the complexity of the link type and corresponds to the time needed to squeeze the linked portion inside the pore. A notable feature is that unlike the translocation of knotted polymers, the passage of the portion of a two-component link that contains the essential crossings typically occurs when the translocation process is half completed. We claim that this difference can be exploited to distinguish knots from links by translocation experiments. These features should help to advance the interpretation and design of future translocation experiments aimed at probing the presence and amount of mutual entanglement in concatenated ring polymers.