Modelling the response of mountain glaciers to anthropogenic or paleo climate change provides valuable insights given their influence on landscapes and water resources. To compensate for the high computational costs when modelling large-scale glaciers, ice fields or ice-sheets over multiple millennia, it is common practice to coarsen the spatial resolution of numerical models to typically 1–20 km, which is not sufficient to describe complex valley topographies. In this paper, we examine the influence of spatial resolution by modelling a growing and retreating ice field at resolutions ranging from 50 m to 2 km using the Instructed Glacier Model (IGM). We find that while ice-covered areas remain similar at all resolutions, ice thickness, flow, and thermal regimes vary non-linearly with altitude in three resolution modes. The highest sensitivity to resolution is characterized by particularly strong changes in simulations within the critical mode at ~400–800 m resolution. At finer resolutions, ice flow is more topographically constrained, resulting in consistently faster flowing and thinner glaciers. In contrast, topographic resampling to coarse resolutions lowers slope angles as well as mountain peaks and raises valley floors, supporting ice growth across all altitudes and prolongating glacial response times. Slower temperature change partially reduces the hysteresis between climate forcing and glacial response but has limited impact on resolution effects. Identifying the critical mode of strong resolution sensitivity is essential, as seemingly stable model results at coarse resolution may be misleading and accurate glacier geometries might arise from parameter choices that compensate for poorly resolved topography. We expect similar non-linear and altitudinal-dependent resolution effects in mountain regions worldwide and emphasize the need for model advances to enable simulations at sufficiently high spatial resolutions to accurately resolve glacier dynamics.