This volume contains a selection of the papers presented at TERMGRAPH 2018, the tenth edition of the international workshop on computing with terms and graphs. Graphs, and graph transformation systems, are used in many areas within Computer Science: to represent data structures and algorithms, to define computation models, as a general modelling tool to study complex systems, etc. Research in this area addresses a range of theoretical and practical issues, including the modelling of first- and higher-order term rewriting by (acyclic or cyclic) graph rewriting, graphical frameworks such as interaction nets and sharing graphs (optimal reduction), rewrite calculi for the analysis of functional programs, graph reduction implementations of programming languages, graphical calculi modelling concurrent and mobile computations, object-oriented systems, graphs as a model of biological or chemical systems, and automated reasoning and symbolic computation systems working on shared structures. Previous editions of TERMGRAPH took place in Barcelona (2002), Rome (2004), Vienna (2006), Braga (2007), York (2009), Saarbrucken (2011), Rome (2013), Vienna (2014) and Eindhoven (2016). TERMGRAPH 2018 is affiliated with FSCD, which is part of FLOC.