In this work, we investigate sensing parameter estimation in the presence of clutter in perceptive mobile networks (PMNs) that integrate radar sensing into mobile communications. Performing clutter suppression before sensing parameter estimation is generally desirable as the number of sensing parameters can be signiffcantly reduced. However, existing methods require high-complexity clutter mitigation and sensing parameter estimation, where clutter is ffrstly identiffed and then removed. In this correspondence, we propose a much simpler but more effective method by incorporating a clutter cancellation mechanism in formulating a sparse signal model for sensing parameter estimation. In particular, clutter mitigation is performed directly on the received signals and the unitary approximate message passing (UAMP) is leveraged to exploit the common support for sensing parameter estimation in the formulated sparse signal recovery problem. Simulation results show that, compared to state-of-theart methods, the proposed method delivers signiffcantly better performance while with substantially reduced complexity.