Clustered cell-free networking, which dynamically partitions the whole network into nonoverlapping subnetworks, has been recently proposed to mitigate the cell-edge problem in cellular networks. However, prior works only focused on optimizing clustered cell-free networking in static scenarios with fixed users. This could lead to a large number of handovers in the practical dynamic environment with moving users, seriously hindering the implementation of clustered cell-free networking in practice. This paper considers user mobility and aims to simultaneously maximize the sum rate and minimize the number of handovers. By transforming the multi-objective optimization problem into a time-varying graph partitioning problem and exploring evolutionary spectral clustering, a temporal-smoothed clustered cell-free networking algorithm is proposed, which is shown to be effective in smoothing network partitions over time and reducing handovers while maintaining similar sum rate.