In mobile multicast transmissions, the receiver with the worst instantaneous channel condition limits the transmission data rate under the desired Quality-of-Service (QoS) constraints. If Automatic Repeat reQuest (ARQ) schemes are applied, the selection of Adaptive Modulation and Coding (AMC) mode will not necessarily be limited by the worst channel anymore, and improved spectral efficiency may be obtained in the efficiency-reliability tradeoff. In this paper, we first propose a Network-Coding-based ARQ (NC-ARQ) scheme in its optimal form and suboptimal form (denoted as Opt-ARQ and SubOpt-ARQ, resp.) to solve the scalability problem of applying ARQ in multicast. Then we propose two joint NC-ARQ-AMC schemes, namely, the Average PER-based AMC (AvgPER-AMC) with Opt-ARQ and AvgPER-AMC with SubOpt-ARQ in a cross-layer design framework to maximize the average spectral efficiency per receiver under specific QoS constraints. The performance is analyzed under Rayleigh fading channels for different group sizes, and numerical results show that significant gains in spectral efficiency can be achieved with the proposed joint NC-ARQ-AMC schemes compared with the existing multicast ARQ and/or AMC schemes.