Many cable management tasks involve separating out the different cables and removing tangles. Automating this task is challenging because cables are deformable and can have combinations of knots and multiple interwoven segments. Prior works have focused on untying knots in one cable, which is one subtask of cable management. However, in this paper, we focus on a different subtask called multi-cable unweaving, which refers to removing the intersections among multiple interwoven cables to separate them and facilitate further manipulation. We propose a method that utilizes visual feedback to unweave a bundle of loosely entangled cables. We formulate cable unweaving as a pick-and-place problem, where the grasp position is selected from discrete nodes in a graph-based cable state representation. Our cable state representation encodes both topological and geometric information about the cables from the visual image. To predict future cable states and identify valid actions, we present a novel state transition model that takes into account the straightening and bending of cables during manipulation. Using this state transition model, we select between two high-level action primitives and calculate predicted immediate costs to optimize the lower-level actions. We experimentally demonstrate that iterating the above perception-planning-action process enables unweaving electric cables and shoelaces with an 84% success rate on average.