Redundant manipulators utilize their redundant solutions to achieve the position and orientation control of the end-effector in a given variety of complex tasks, which is an essential issue in the field of industrial robots. Moreover, for manipulators with unknown models, traditional control methods generate large control errors during the execution of the task or even lead to the failure of the task. To address this problem, this paper proposes a Discrete Data-Driven Position and Orientation Control (D³POC) scheme. The scheme consists of a Discrete Jacobian Matrix Learning (DJML) algorithm, a Discrete Gradient Neural Dynamics (DGND) solver, and a Kalman filter. Then, theoretical analyses are provided to demonstrate the convergence of the D³POC scheme. Subsequently, simulations, comparisons, and experiments based on this scheme are carried out on redundant manipulators. The obtained results indicate the validity, superiority, and practicability of the proposed control scheme.