We have experimentally demonstrated the first non-intrusive 1-GeV proton beam extraction for the generation of muons with a temporal structure optimized for Muon Spin Relaxation/Rotation/Resonance (MuSR) applications. The proton pulses are extracted based on the laser neutralization of 1 GeV hydrogen ion (H-) beam in the high energy beam transport of the Spallation Neutron Source (SNS) accelerator. The maximum flux of the extracted proton beam accounts for only 0.2% of the total proton beam used for neutron production, a marked difference from the 20% reduction at other co-located muon and neutron facilities, and thus the proposed method will result in negligible impact on the SNS operation. This paper describes the development of a fiber/solid-state hybrid laser system that has high flexibility of pulse structure and output power, initial experiments on laser neutralization of H- beam and separation of H0 beam from the existing SNS accelerator beam line, conversion of H0 to proton at the SNS linac dump, and measurement results of 30 ns/50 kHz proton pulses. This system conclusively demonstrates the feasibility of laser-based proton beam extraction to power a world-leading MuSR facility at the SNS.