Solar particle events (SPEs) are short-lived bursts of high-energy particles from the solar atmosphere and are widely recognized as posing significant economic risks to modern society. Most SPEs are relatively weak and have minor impacts on the Earth's environment, but historic records contain much stronger SPEs which have the potential to alter atmospheric chemistry, impacting climate and biological life. The impacts of such strong SPEs would be far more severe when the Earth's protective geomagnetic field is weak, such as during past geomagnetic excursions or reversals. Here, we model the impacts of an extreme SPE under different geomagnetic field strengths, focusing on changes in atmospheric chemistry and surface radiation using the atmosphere-ocean-chemistry-climate model SOCOL3-MPIOM and the radiation transfer model LibRadtran. Under current geomagnetic conditions, an extreme SPE would increase NO x concentrations in the polar stratosphere and mesosphere, causing reductions in extratropical stratospheric ozone lasting for about a year. In contrast, with no geomagnetic field, there would be a substantial increase in NO x throughout the entire atmosphere, resulting in severe stratospheric ozone depletion for several years. The resulting ground-level ultraviolet (UV) radiation would remain elevated for up to 6 y, leading to increases in UV index up to 20 to 25% and solar-induced DNA damage rates by 40 to 50%. The potential evolutionary impacts of past extreme SPEs remain an important question, while the risks they pose to human health in modern conditions continue to be underestimated.