This paper addresses joint estimation of the frequency and the direction-of-arrival (DOA), under the relaxed condition that both snapshots in the temporal domain and sensors in the spacial domain are sparsely spaced. Specifically, a novel coprime sparse array allowing a large range for interelement spacings is employed in the proposed joint scheme, which greatly alleviates the conventional array's half-wavelength constraint. Further, by incorporating small-sized DFT spectrum correction with the closed-form robust Chinese Remainder Theorem (CRT), both spectral aliasing and integer phase ambiguity caused by spatio-temporal under-sampling can be removed in an efficient way. As a result, these two parameters can be efficiently estimated by reusing the observation data collected in parallel at different undersampling rates, which remarkably improves the data utilization. Numerical results demonstrate that the proposed joint scheme is highly accurate.