Dynamic networks, where ties can be shed and new ties can be formed, promote the evolution of cooperation. Yet, past research has only compared networks where all ties can be severed to those where none can, confounding the benefits of fully dynamic networks with the presence of some dynamic ties within the network. Further, humans do not live in fully dynamic networks. Instead, in real-world networks, some ties are subject to change, while others are difficult to sever. Here, we consider whether and how cooperation evolves in networks containing both static and dynamic ties. We argue and find that the presence of dynamic ties in networks promotes cooperation even in static ties. Consistent with previous work demonstrating that cooperation cascades in networks, our results show that cooperation is enhanced in networks with both tie types because the higher rate of cooperation that occurs following the dynamics process “spills over” to those relations that are more difficult to alter. Thus, our findings demonstrate the critical role that dynamic ties play in promoting cooperation by altering behavioral outcomes even in non-dynamic relations.