The K-staged two-dimensional cutting stock problem with variable sheet size (K-2CSV) represents a common problem in industry where a cutting pattern to cut rectangular shaped elements out of large stock sheets is required. The NP-hard nature of the problem makes it difficult to find a good pattern, which directly translates to unused waste material of the stock sheet. The historical approach is to try and find an optimal pattern through dynamic programming, which later was supplemented by Branch-and-Bound and heuristic approaches. In this paper we develop a bottom-up Branch-and-Bound approach, creating an optimal cutting pattern for a singular stock sheet. While top-down approaches sucessively subdivide the sheet into smaller rectangles and ultimately into the required elements, bottom-up approaches combine elements and combinations thereof together to create whole patterns. The process is supplemented with a general framework to integrate it into the implementation of the Algorithms and Complexity Group at the TU Wien. The framework allows to solve problem instances spanning multiple stock sheets by applying the algorithm multiple times. We then boost the performance of the algorithm by improving the used lower and upper bounds as well as reducing the search space through the detection of dominated or duplicate patterns. Lastly, using different settings we apply the algorithm to problem instances taken from the literature to obtain computational results.