You can deploy a Spring MVC application with Spring Data Neo4j on Heroku by making your application self-hosting, accessing Heroku environment variables for configuration, and deploying to the cloud. To make your application self-hosting, you need to add dependencies for Jetty to your pom.xml file, create a launch script using the appassembler-maven-plugin, and modify the Spring application context to use Neo4j environment variables. After that, you can deploy to Heroku by creating a Procfile, initializing a local git repository, provisioning a Heroku stack, adding the Neo4j Add-on, and deploying your application. Once deployed, you can access your Neo4j graph through Heroku's Webadmin using the NEO4J_URL environment variable.