Glaciers expel sediment as they melt, in addition to ice and water. As a result, changing glacier dynamics and melt produce changes to glacier erosion and sediment discharge, which can impact the landscape surrounding retreating glaciers, as well as communities and ecosystems downstream. Currently, numerical models that transport subglacial sediment on sub-hourly to decadal scales are one-dimensional, usually along a glacier's flow line. Such models have proven useful in describing the formation of glacial landforms, the impact of sediment transport on glacier dynamics, and the interactions among climate, glacier dynamics, and erosion. However, these models omit the two-dimensional spatial distribution of sediment and its impact on sediment connectivity – the movement of sediment between its detachment in source areas and its deposition in sinks. Here, we present a numerical model that fulfills a need for predictive frameworks that describe subglacial sediment discharge in two spatial dimensions (x and y) over time. SUGSET_2D evolves a two-dimensional subglacial till layer in response to bedrock erosion and changing sediment transport conditions. Numerical experiments performed using an idealized alpine glacier illustrate the heterogeneity in sediment transport and bedrock erosion below the glacier. An increase in sediment discharge follows increased glacier melt, as has been documented in field observations and other numerical experiments. We also apply the model to a real alpine glacier, Griesgletscher in the Swiss Alps, where we compare outputs with annual measurements of sediment discharge. SUGSET_2D accurately reproduces the general quantities of sediment discharge and the year-to-year sediment discharge pattern measured at the glacier terminus. The model's ability to match the measured data depends on the tunable sediment grain size parameter, which controls subglacial sediment transport capacity. Smaller grain sizes allow sediment transport to occur in regions of the bed with reduced water flow and channel size, effectively increasing sediment connectivity into the main channels. The model provides the essential components of modeling subglacial sediment discharge on seasonal to decadal timescales and reveals the importance of including spatial heterogeneities in water discharge and sediment transport in both the x and y dimensions in evaluating sediment discharge.