A new relativistic vortex cutter driven by the Laguerre-Gaussian (LG) mode is carried out for the first time in three-dimensional particle-in-cell simulations. Studies show that the electric fields periodically concentrate and emanate within every laser wavelength for the reflected circularly polarized LG_{p}^{l} (p=0, l=1, σ_{z}=-1) laser, which works just like a vortex cutter, resulting in a relativistic ultrashort collimated electron cluster with a constant period in space. A single particle model is given and verifies that the cluster formation has a close relation with the parameters of orbital angular momentum (l) and spin angular momentum (σ_{z}). Such a relativistic vortex cutter potentially can be applied for the accelerator, generating high-flux particle and coherent radiation sources, and so on.