Recent developments in 3D shape representation opened new possibilities for generating detailed 3D shapes. Despite these advances, there are few studies dealing with the generation of 4D dynamic shapes that have the form of 3D objects deforming over time. To bridge this gap, we focus on generating 4D dynamic shapes with an emphasis on both generation quality and efficiency in this paper. HyperDiffusion, a previous work on 4D generation, proposed a method of directly generating the weight parameters of 4D occupancy fields but suffered from low temporal consistency and slow rendering speed due to motion representation that is not separated from the shape representation of 4D occupancy fields. Therefore, we propose a new neural deformation representation and combine it with conditional neural signed distance fields to design a 4D representation architecture in which the motion latent space is disentangled from the shape latent space. The proposed deformation representation, which works by predicting skinning weights and transformation matrices for multiple parts, also has advantages over the deformation modules of existing 4D representations in understanding the structure of shapes. In addition, we design a training process of a diffusion model that utilizes the shape and motion features that are extracted by our 4D representation as data points. The results of unconditional generation, conditional generation, and motion retargeting experiments demonstrate that our method not only shows better performance than previous works in 4D dynamic shape generation but also has various potential applications. The project page for this paper is available at https://anonymous-pp.github.io/.