Controlling electronic processes in low-dimension electron systems is centrally important for both fundamental and applied researches. While most of the previous works focused on SrTiO3-based two-dimensional electron gases (2DEGs), here we report on a comprehensive investigation in this regard for amorphous-LaAlO3/KTaO3 2DEGs with the Fermi energy ranging from 13 meV to 488 meV. The most important observation is the dramatic variation of the Rashba spin–orbit coupling (SOC) as Fermi energy sweeps through 313 meV: The SOC effective field first jumps and then drops, leading to a cusp of 2.6 T. Above 313 meV, an additional species of mobile electrons emerges, with a 50-fold enhanced Hall mobility. A relationship between spin relaxation distance and the degree of band filling has been established in a wide range. It indicates that the maximal spin precession length is 70.1 nm and the maximal Rashba spin splitting energy is 30 meV. Both values are much larger than the previously reported ones. As evidenced by density functional theory calculation, these unusual phenomena are closely related to the distinct band structure of the 2DEGs composed of 5d electrons. The present work further deepens our understanding of perovskite conducting interfaces, particularly those composed of 5d transition-metal oxides.