This post describes the necessary stops to deploy a Mule application to WebSphere Application Server(In this case 7.x and Mule 3.3.x, both older version of each products so may need less/additional changes for newer versions) and some additional steps if you are using certain modules such as CXF.
Enable parent last class loading
Only do this at the MODULE level. Navigate to:
Application Types > WebSphere enterprise applications > swaggerProject_war > Modules > Manage Modules > myApp.war
Classes loaded with local class loader first (parent last) Apply and Save directly to the master configuration.
Exclude Servlet APIs and Geronimo Stax lib
Disable IBM JAXWS Engine
Modify the configuration of the maven-war-plugin to add a manifest entry to shut off activation of IBM WSAS' JAX-WS engine. (Add the following manifestEntries element to the maven-war-plugin configuration:
Add additional JVM/Endorsed dependencies