In this paper, we analyze in detail a solar jet event triggered by magnetic reconnections in the lower atmosphere of the Sun. On 1 August 2014, the solar jet occurred at a satellite sunspot on the edge of the National Oceanic and Atmospheric Administration (NOAA) active region 12127. It was composed of an Hα surge, an ultra-violet (UV) jet, and Extra Ultra-violet (EUV) hot, and cool jets. The TiO images taken by the Goode Solar Telescope (GST) at the Big Bear Solar Observatory (BBSO) show that the satellite sunspot has successively decayed during the solar jet, and its area reduced by 80$%$ till the end of the jet. Line-of-sight photospheric magnetic field observations by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) show that the negative magnetic polarity corresponding to the satellite sunspot was obviously cancelled with the adjacent positive magnetic field, which might result in the brightenings of the jet footpoint source. According to the observations by the Atmospheric Imaging Assembly (AIA) onboard SDO, the footpoint brightenings firstly appeared at 1600{\AA