The growing scale of applications encoded to Boolean Satisfiability (SAT) problems imposes the need for accelerating SAT simplifications or preprocessing. Parallel SAT preprocessing has been an open challenge for many years. Therefore, we propose novel parallel algorithms for variable and subsumption eliminations targeting Graphics Processing Units (GPUs). We implemented the new algorithms in a tool called SIGmA. Benchmarks show that SIGmA achieves an acceleration of 66x over a state-of-the-art SAT simplifier (SatELite). Regarding SAT solving, we have conducted a thorough evaluation, comparing SIGmA in combination with MiniSat to SatELite, and studying the impact of SiGmA on the solvability of Lingeling. We conclude that our algorithms have a considerable impact on the solvability of SAT problems.