With the increasing demand for garbage classification, images and videos are required to complement each other in realtime scenarios. Therefore, the research of garbage detection and classification is still of long-term value. This paper introduces a novel garbage detection and sorting framework called MCMM that incorporates multi-column convolution and matrix-multiplication (MatMul)-free based Transformer. Specially, the multi-column convolution is designed to enhance the performance of image processing tasks through multi-scale feature extraction and adaptation to objects of varying sizes. MatMul-free Transformer significantly reduces computational complexity and hardware overhead by eliminating matrix multiplication, while maintaining high model performance. The experimental evaluation shows that the MCMM network achieves better results in both qualitative and quantitative methods compared to existing competing methods.