Monitoring glacier dynamics is an effective approach for quantifying the response of the glaciers in cold arid mountainous areas to climate change. However, the quantification of short-term flow dynamics of the mountain glaciers in cold-dry climates has rarely been reported. This article investigated the intra-annual flow dynamics in terms of velocity and ice thickness changes on the Kunlun glacier, a mountain glacier in the cold-dry west Kunlun mountains, using spaceborne synthetic aperture radar (SAR) imagery. We applied the improved pixel-offset-tracking small-baseline-subset method (PO-SBAS) on ascending and descending Sentinel-1A SAR images acquired in 2017 and 2018 to estimate the three-dimensional (i.e., north–south, west–east, and vertical) velocity time series of the glacier. The vertical velocities were further decomposed into the surface-parallel-flow (SPF) and the nonsurface-parallel-flow (nSPF) components, which link glacier motion along glacier surface slope and internal ice deformation, respectively, to glacier thickness changes. Our findings show that the eastern branch of the glacier moved faster than the western branch. We inferred that a loss of ice thickness due to a previous surge on the western branch should be responsible for its slower flow. The nSPF rates are higher than the SPF rates in both branches, indicating that internal ice deformation primarily controls the changes in ice thickness. We also observed an apparent summer acceleration in the nSPF rates, which is likely caused by changes in subglacial hydrological conditions. This article highlights the potential uses of the improved PO-SBAS method of quantifying the flow dynamics of the glaciers in cold-dry mountain regions.