By introducing Caching as a Service (CaaS) in Cloud radio access network (C-RAN), the joint resource segmentation and transmission rate adaptation problem is investigated in this paper. Specifically, in the baseband unit (BBU) pool of C-RAN, we optimally segment computation and storage resources to different types of virtual machines (VMs), and in the remote radio heads (RRHs), we adjust the beamformers to obtain the cache-based adaptive rate (CBAR). We aim to minimize the system cost, which includes server cost, VM cost and wireless transmission cost. The joint optimization problem is formulated as a mixed-integer nonlinear programming (MINLP) problem, which contains $l_0$-norm terms in the objective function and nonconvex constraints. We propose a three-step solution approach, i.e., a general smooth function approximation step, a weighted minimum mean square error (WMMSE) reformulation step and an integer recovery step. Simulation results show that our proposed integer recovery algorithms recover the integer variable values effectively.