The sound field separation methods can separate the target field from the interfering noises, facilitating the study of the acoustic characteristics of the target source, which is placed in a noisy environment. However, most of the existing sound field separation methods are derived in the frequency-domain, thus are best suited for separating stationary sound fields. In this paper, a time-domain sound field separation method is developed that can separate the non-stationary sound field generated by the target source over a sphere in real-time. A spherical array sets up a boundary between the target source and the interfering sources, such that the outgoing field on the array is only generated by the target source. The proposed method decomposes the pressure and the radial particle velocity measured by the array into spherical harmonics coefficients, and recoveries the target outgoing field based on the time-domain relationship between the decomposition coefficients and the theoretically derived spatial filter responses. Simulations show the proposed method can separate non-stationary sound fields both in free field and room environments, and over a longer duration with small errors. The proposed method could serve as a foundation for developing future time-domain spatial sound field manipulation algorithms.