The application of multiple-input multiple-output (MIMO) over orthogonal time frequency space (OTFS) modulation is envisioned to provide high-data-rate wireless transmission in high-mobility environments. However, in these communication scenarios, the multiple-dimensional interference, which can generate from space, delay and Doppler domains, challenges the channel equalization and symbol detection at the MIMO-OTFS receiver. To tackle this issue, we propose a time-space domain channel equalizer, relying on the mathematical least squares minimum residual algorithm, to remove the channel distortion on data symbols. The proposed channel equalizer adopts a recursion method to achieve symbol estimates, which can realize fast convergence by leveraging the sparsity of MIMO-OTFS channel matrix. Instead of directly remapping the equalized OTFS symbols into data bits, we develop an enhanced data detection (EDD) scheme to iteratively demodulate the superposed multi-antenna signal. The EDD can not only realize the linear-complexity interference cancellation, but also efficiently reap the spatial and multi-path diversities of MIMO-OTFS channel. The simulations show the proposed channel equalization and EDD algorithms enable the MIMO-OTFS receiver to robustly demodulate multi-stream 256-ary quadrature amplitude modulation symbols, under a maximum velocity of 550 km/h at 5.9 GHz carrier frequency.