The realization of spatiotemporal vortex structure of various physical fields with transverse orbital angular momentum (OAM) has attracted much attention and is expected to expand the research scope and open new opportunities in their respective fields. Here we present theoretically the first, to the best of our knowledge, study on the generation of attosecond pulse trains featuring a spatiotemporal optical vortex (STOV) structure by a two-color femtosecond light field, with each color carrying transverse OAM. Through careful optimization of relative phase and intensity ratio, we validate the efficient upconversion of the infrared pulse into its tens of order harmonics, showing that each harmonic preserves a corresponding intact topological charge. This unique characteristic enables the synthesis of an extreme ultraviolet attosecond pulse train with transverse OAM. In addition, we reveal that ionization depletion plays an outsize role therein. Our studies pave the way for the generation and utilization of light fields with STOV in the attosecond regime.