In this paper, we present Nyx, the first system to both effectively mitigate modern Distributed Denial of Service (DDoS) attacks regardless of the amount of traffic under adversarial control and function without outside cooperation or an Internet redesign. Nyx approaches the problem of DDoS mitigation as a routing problem rather than a filtering problem. This conceptual shift allows Nyx to avoid many of the common shortcomings of existing academic and commercial DDoS mitigation systems. By leveraging how Autonomous Systems (ASes) handle route advertisement in the existing Border Gateway Protocol (BGP), Nyx allows the deploying AS to achieve isolation of traffic from a critical upstream AS off of attacked links and onto alternative, uncongested, paths. This isolation removes the need for filtering or de-prioritizing attack traffic. Nyx controls outbound paths through normal BGP path selection, while return paths from critical ASes are controlled through the use of specific techniques we developed using existing traffic engineering principles and require no outside coordination. Using our own realistic Internet-scale simulator, we find that in more than 98% of cases our system can successfully route critical traffic around network segments under transit-link DDoS attacks; a new form of DDoS attack where the attack traffic never reaches the victim AS, thus invaliding defensive filtering, throttling, or prioritization strategies. More significantly, in over 95% of those cases, the alternate path provides complete congestion relief from transit-link DDoS. Nyx additionally provides complete congestion relief in over 75% of cases when the deployer is being directly attacked.