Safe spacecraft rendezvous requires the chaser to satisfy stringent path constraints during proximity operations while preserving convergence to the docking state. Although high-order control barrier functions (HOCBFs) provide a systematic way to enforce safety, their monolithic constraint at the final control input level can lead to boundary riding behavior and degraded transient performance in path constrained rendezvous scenarios. This paper proposes a cascaded control barrier function (CCBF) framework for safe spacecraft rendezvous. By decomposing the safety constraint into sequential cascade layers, the proposed approach enforces safety consistency from the virtual control level to the actual force input, thereby improving design traceability and tuning tractability compared with conventional HOCBF formulations. The method is applied to satellite rendezvous scenarios subject to a semi-cubical cone path constraint, within a backstepping based sequential control Lyapunov function-quadratic programming (CLF-QP) architecture. Numerical simulation demonstrates that both HOCBF and the proposed CCBF maintain the prescribed safety corridor, whereas the proposed CCBF yields smoother and faster convergence to the docking region with reduced boundary-riding behavior under the same path constraint.