Defect-carrier interaction in transition metal dichalcogenides (TMDs) plays important roles in carrier relaxation dynamics and carrier transport, which determines the performance of electronic devices. With femtosecond laser time-resolved spectroscopy, we investigated the effect of grain boundary/edge defects on the ultrafast dynamics of photoexcited carrier in molecular beam epitaxy (MBE)-grown MoTe2 and MoSe2. We found that, comparing with exfoliated samples, the carrier recombination rate in MBE-grown samples accelerates by about 50 times. We attribute this striking difference to the existence of abundant grain boundary/edge defects in MBE-grown samples, which can serve as effective recombination centers for the photoexcited carriers. We also observed coherent acoustic phonons in both exfoliated and MBE-grown MoTe2, indicating strong electron-phonon coupling in this materials. Our measured sound velocity agrees well with the previously reported result of theoretical calculation. Our findings provide a useful reference for the fundamental parameters: carrier lifetime and sound velocity and reveal the undiscovered carrier recombination effect of grain boundary/edge defects, both of which will facilitate the defect engineering in TMD materials for high speed opto-electronics.