Synthesis route planning is in the core of chemical intelligence that will power the autonomous chemistry platforms. In this task, we rely on algorithms to generate possible synthesis routes with the help of retro- and forward-synthetic approaches. Generated synthesis routes can be merged into a synthesis graph which represents theoretical pathways to the target molecule. However, it is often required to modify a synthesis graph due to typical constraints. These constraints might include "undesirable substances", e.g., an intermediate that the chemist does not favor or substances that might be toxic. Consequently, we need to prune the synthesis graph by the elimination of such undesirable substances. Synthesis graphs can be represented as directed (not necessarily acyclic) bipartite graphs, and the pruning of such graphs in the light of a set of undesirable substances has been an open question. In this study, we present the Synthesis Graph Pruning (SGP) algorithm that addresses this question. The input to the SGP algorithm is a synthesis graph and a set of undesirable substances. Furthermore, information for substances is provided as metadata regarding their availability from the inventory. The SGP algorithm operates with a simple local rule set, in order to determine which nodes and edges need to be eliminated from the synthesis graph. In this study, we present the SGP algorithm in detail and provide several case studies that demonstrate the operation of the SGP algorithm. We believe that the SGP algorithm will be an essential component of computer aided synthesis planning.