Network slicing is a technology that virtualizes a single infrastructure into multiple logical networks (called slices) where resources or virtualized functions can be flexibly configured by demands of applications to satisfy their quality of service (QoS) requirements. Generally, to provide the guaranteed QoS in applications, resources of slices are isolated. In wired networks, this resource isolation is enabled by allocating dedicated data bandwidths to slices. However, in wireless networks, resource isolation may be challenging because the interference between links affects the actual bandwidths of slices and degrades their QoS. In this paper, we propose a slice management scheme that mitigates the interference imposed on each slice according to their priorities by determining routes of flows with a different routing policy. Traffic flows in the slice with the highest priority are routed into shortest paths. In each lower-priority slice, the routing of traffic flows is conducted while minimizing a weighted summation of interference to other slices. Since higher-priority slices have higher interference weights, they receive lower interference from other slices. As a result, the QoS of slices is differentiated according to their priorities while the interference imposed on slices is reduced. We compared the proposed slice management scheme with a naïve slice management (NSM) method that differentiates QoS among slices by priority queuing. We conducted some simulations and the simulation results show that our proposed management scheme not only differentiates the QoS of slices according to their priorities but also enhances the average throughput and delay performance of slices remarkably compared to that of the NSM method. The simulations were conducted in grid network topologies with 16 and 100 nodes and a random network topology with 200 nodes. Simulation results indicate that the proposed slice management increased the average throughput of slices up to 6%, 13%, and 7% and reduced the average delay of slices up to 14%, 15%, and 11% in comparison with the NSM method.