Cascaded random Raman fiber lasers (CRRFLs) have been used as a new platform for designing high power and wavelength-agile laser sources. Recently, CRRFL pumped by ytterbium-doped random fiber laser (YRFL) has shown both high power output and low relative intensity noise (RIN). Here, by using a wavelength- and bandwidth-tunable point reflector in YRFL, we experimentally investigate the impacts of YRFL on the spectral and RIN properties of the CRRFL. We verify that the bandwidth of the point reflector in YRFL determines the bandwidth and temporal stability of YRFL. It is found that with an increase in the bandwidth of the point reflector in YRFL from 0.2 nm to 1.4 nm, CRRFL with higher spectral purity and lower RIN can be achieved due to better temporal stability of YRFL pump. By broadening the point reflector’s bandwidth to 1.4 nm, the lasing power, spectral purity, and RIN of the 4th-order random lasing at 1 349 nm can reach 3.03 W, 96.34%, and –115.19 dB/Hz, respectively. For comparison, the spectral purity and RIN of the 4th-order random lasing with the point reflector’s bandwidth of 0.2 nm are only 91.20% and –107.99 dB/Hz, respectively. Also, we realize a wavelength widely tunable CRRFL pumped by a wavelength-tunable YRFL. This work provides a new platform for the development of ideal distributed Raman amplification pump sources based on CRRFLs with both good temporal stability and wide wavelength tunability, which is of great importance in applications of optical fiber communication and distributed sensing.