Subglacial water modulates glacier velocity across a wide range of space and time scales by influencing friction at the glacier bed. Observations show ice acceleration due to supraglacial lake drainage and water draining through moulins, where both configurations involve water inputs to the bed. Here we consider the reverse: water extraction from the subglacial system. Removing subglacial water results in different dynamics than injecting water, and we hypothesize that understanding these processes will allow for improved characterization of the physics of subglacial hydrology. Water extraction is a proposed intervention method for slowing glaciers that requires significant further investigation before it should be tested or implemented in the field. Here we set up model experiments in the Subglacial Hydrology And Kinetic, Transient Interactions (SHAKTI) model coupled with the Ice-sheet and Sea-level System Model (ISSM). By analyzing the problem of an isolated borehole in a background pressure field to determine the region of extraction influence, we find an analytical solution which shows that the water pressure returns to the background value approximately as a logarithm with distance. The benefit of the analytical solution is that the dependence of uncertain parameters is clear and may be used to constrain subglacial hydrology models. We find good agreement between this analytical result and full SHAKTI simulations. Using the coupled SHAKTI-ISSM model, we perform transient model experiments on an idealized tidewater glacier geometry and on Helheim Glacier in Greenland to determine the effects of water extraction on glacier velocity. With continuous pumping, we simulate a modest impact on velocity, which is sensitive to the extraction rate and site location. The response time to pumping initiation and the recovery time following cessation scale according to effective pressure, with typical times on the order of hours to days. These results are encouraging that water extraction is a method of probing the subglacial hydrologic system to better constrain the uncertain physics, with further research required to determine if it is an effective intervention method.