This paper proposes ACC-AMG, an optimized AMG framework that further improves the efficiency of sparse general matrix-matrix multiplication (SpGEMM) on modern GPUs. Considering that SpGEMM is a major bottleneck in the AMG setup phase, we propose a performance-model-based method that takes the multi-dimensional features of two matrix blocks as input and maps each block-level computation to the most suitable computing unit, i.e., Tensor Cores (TCs) or CUDA Cores (CCs). To better exploit this adaptive execution strategy, ACC-AMG further incorporates targeted register-pressure reduction for CC execution, a block-wise load-balancing scheme for TC execution, and mixed-precision support. To better utilize algorithm components in existing libraries, ACC-AMG is integrated into the hypre framework.