In order to realize high-speed cutting of silicon carbide (SiC) wafers, stealth dicing experiments were carried out by using self-developed high-energy picosecond pulsed fiber lasers. According to the cross-section topography, surface thermal damage area and edge straightness of the slices, cutting results of the picosecond lasers were analyzed, and the effects of single pulse energy and scanning speed on the slice quality were explored. The results showed that when a picosecond laser with center wavelength of 1030 nm, repetition rate of 100 kHz, pulse energy of 20 μJ, and pulse width of about 100 ps was used for stealth dicing of a SiC wafer with thickness of 360 μm. The quality of the slices can meet the requirements of practical applications. The scanning speed can reach 400 mm/s and the corresponding cutting speed was 44.44 mm/s, which was higher than other related reports.