Considering the ever-increasing data size, the traditional subspace-based frequency-modulated continuous wave (FMCW) multiple-input multiple-output (MIMO) radar parameter estimation method is no longer suitable, due to its high computation complexity in eigenvalue decomposition and multidimensional spectrum peak search, which makes it difficult to process the data in real time. In addition, with this method, the accuracy of parameter estimation is also limited by the subspace orthogonality. In order to solve such problems, this paper takes Texas instruments (TI) cascade FMCW MIMO radar system with a large data size as the research object, derives and establishes a tensor domain data model, and designs a fast joint estimation method for direction-of-arrival (DOA), velocity, and range, using the compressed parallel factorization (PARAFAC) technique. Firstly, a data model conforming to the TI radar hardware is established, and its tensor domain model is obtained. Then, the Tucker3 decomposition is used to substantially compress the dimension of original tensor, to obtain a compressed tensor model. After that, the trilinear decomposition problem is solved by trilinear alternating least square (TALS), following by its decompression to original tensor dimension. Finally, the parameter estimation is achieved by phase extraction. Furthermore, in order to minimize the effect of ground clutter and interference on the received signal, a data domain beamforming is employed. Simulations and experiment were carried out to validate the computational efficiency and effectiveness of the proposed method.