Low Earth orbit (LEO) satellite networks will become the core infrastructure of space-air-ground integrated networks in 6G wireless technology, providing ubiquitous broadband internet services for global users in a cost-effective manner. However, timing synchronization is a significant problem in large-scale multisatellite (MSAT) communications. Due to the different propagation delays, signals transmitted from multiple satellites to a user terminal are always misaligned. In this paper, we study asynchronous satellite-terrestrial interference in LEO MSAT systems, aiming to mitigate asynchronous interference through cooperative beamforming. Specifically, we derive an MSAT coherent transmission model and analyse the power degeneration of interference due to the offset sample time. We also derive the closed-form expression for the achievable rate by considering asynchrony and propose a cooperative beamforming algorithm based on the weighted minimum mean square error (WMMSE) criterion. To realize accurate timing advance (TA), we design a delay estimation method based on pseudorandom code. Finally, we approximate the achievable rate under an imperfect TA and propose a timing-error-robust algorithm. The simulation results show that the proposed asynchronous algorithm achieves a 21.47% performance improvement over the conventional algorithm, indicating that by exploiting time asynchrony, we can naturally eliminate some interference and achieve substantial performance improvements.