Cut should be enough. Start the cut, zoom out if necessary, move the cursor to the general location of the destination vertex and press "I" (which will centre the viewport on the cursor). Zoom in, complete the cut. Obviously you must not click any of the mouse buttons during that procedure except for clicking the 2 vertices.
Or, select the 3 vertical edges, Connect, use Snap to Vertex with Axis Constraints on (click and drag on the Z axis handle of the Gizmo, not on its centre) and snap to one of the existing vertices. Weld the end vertices as there'll be 2 of them.
Or, upgrade to 2013 because that annoying "MMB cancels the current operation" has finally been fixed
😉
Max 2016 (SP1/EXT1)
Win7Pro x64 (SP1). i5-3570K @ 4.4GHz, 8Gb Ram, DX11.
nVidia GTX760 (2GB) (Driver 430.86).