This paper considers the one-dimensional cutting stock problem (1D-CSP) with divisible items, which arises in the steel industries. While planning the steel cutting operations, each item can be divided into smaller pieces, then they can be recombined by welding. The objective is to minimize both the trim loss and the number of the welds. The problem can be seen as a natural generalization of the cutting stock problem (CSP) with skiving option  where recombining operation has a cost. In this paper, a mathematical model for the problem is given and a dynamic programming based heuristic algorithm is proposed in accordance with the company needs. Furthermore, a software, which is based on the proposed heuristic algorithm, is developed to use in MKA Company, and its performance is analyzed by solving real-life problems in the steel industry. The computational experiments show the efficiency of the proposed algorithm.