We discuss here the realization of electrically tunable beam focusing and splitting using a single graphene flake with operation in the terahertz regime. The required conductivity pattern along a strip on the background graphene layer for focusing and splitting phenomena is created by the proper design of an uneven ground plane. The strip is illuminated with a guided surface plasmon polaritons (SPPs) plane wave and the physical origin of the design procedure is evaluated from the phase of effective mode index of propagating SPP wave. Upon tuning the applied gate voltage between the graphene sheet and the substrate the modulation of splitting angle and focal length (FL) is achieved. Finite-Difference Time-Domain (FDTD) numerical method is employed to explore the propagation characteristic of SPP waves. Such one-atom-thick devices with the capability of electrical manipulation of light beam besides the compatibility with current planar optoelecetronic systems can find valuable potential applications in the field of transformational plasmon optics.