Edge service caching can effectively reduce the delay or bandwidth overhead for acquiring and initializing applications. To address single-base station (BS) transmission limitation and serious edge effect in traditional cellular-based edge service caching networks, in this paper, we proposed a novel user-centric edge service caching framework where each user is jointly provided with edge caching and wireless transmission services by a specific BS cluster instead of a single BS. To minimize the long-term average delay under the constraint of the caching cost, a mixed integer non-linear programming (MINLP) problem is formulated by jointly optimizing the BS clustering and service caching decisions. To tackle the problem, we propose JO-CDSD, an efficiently joint optimization algorithm based on Lyapunov optimization and generalized benders decomposition (GBD). In particular, the long-term optimization problem can be transformed into a primal problem and a master problem in each time slot that is much simpler to solve. The near-optimal clustering and caching strategy can be obtained through solving the primal and master problem alternately. Extensive simulations show that the proposed joint optimization algorithm outperforms other algorithms and can effectively reduce the long-term delay by at most $93.75% and caching cost by at most $53.12%.