  While general relativity predicts only two tensor modes for gravitational
wave polarization, general metric theories of gravity allows up to four
additional modes, including two vector and two scalar modes. Observing the
polarization modes of gravitational waves could provide a direct test of the
modified gravity. The stochastic gravitational wave background (SGWB), which
may be detected by space-based laser-interferometric detectors at design
sensitivity, will provide an opportunity to directly measure alternative
polarization. In this paper, we investigate the performance of the LISA-TianQin
network for detecting alternative polarizations of stochastic backgrounds, and
propose a method to separate different polarization modes. First, we generalize
the small antenna approximation to compute the overlap reduction functions for
SGWB with arbitrary polarization, which is suitable for any time-delay
interferometry combination. Then we analyze the detection capability of
LISA-TianQin for SGWB with different polarizations. Based on the LISA-TianQin
orbital characteristics, we propose a method to distinguish different
polarization modes from their mixed data. Compared with ground-based detectors,
the LISA-TianQin network is more capable of resolving polarizations of SGWB. In
particular, the LISA-TianQin network has the potential to resolve two scalar
modes that ground-based detectors cannot.
