Observing that the existing model compression approaches only focus on reducing the redundancies in convolutional neural networks (CNNs) along one particular dimension (e.g., the channel or spatial or temporal dimension), in this work, we propose our multidimensional pruning (MDP) framework, which can compress both 2-D CNNs and 3-D CNNs along multiple dimensions in an end-to-end fashion. Specifically, MDP indicates the simultaneous reduction of channels and more redundancy on other additional dimensions. The redundancy of additional dimensions depends on the input data, i.e., spatial dimension for 2-D CNNs when using images as the input data, and spatial and temporal dimensions for 3-D CNNs when using videos as the input data. We further extend our MDP framework to the MDP-Point approach for compressing point cloud neural networks (PCNNs) whose inputs are irregular point clouds (e.g., PointNet). In this case, the redundancy along the additional dimension indicates the point dimension (i.e., the number of points). Comprehensive experiments on six benchmark datasets demonstrate the effectiveness of our MDP framework and its extended version MDP-Point for compressing CNNs and PCNNs, respectively.