The realization of fully coherent light sources at extreme ultraviolet to x-ray region has been a long-standing challenge for laser technologies. While modern single pass free-electron lasers (FELs) hold the ability to produce very intense x-ray radiation on few-femtosecond timescale, the output radiation pulses usually have noisy spectra and limited temporal coherence since the amplification starts from electron noise. A promising way for producing stable transform-limited pulses is based on the harmonic up-conversion techniques with a conventional laser as the seed. However, it is found that the insignificant phase error in the seed laser may be eventually multiplied by the harmonic number, leading to a degradation of the output temporal coherence at x-ray wavelength. Here, we report for the first time on the demonstration of a slippage boosted spectral cleaning technique to mitigate the impact of seed laser induced phase errors and to significantly improve the temporal coherence of a seeded FEL with large phase errors in the seed laser. Experimental results indicate the possibility of generating fully coherent x-ray radiation pulses with this technique.