Drone itself is not capable of this. There are 3 different approaches:
1/ Arquillian Warp allows combination of server side and client side testing arquillian.github.com/docs/warp.adoc at warp-docs · lfryc/arquillian.github.com · GitHub
2/ Deploying "mocked facade" in your application - e.g. preparing alternative CDI Bean or deploying completely different class content
3/ Arquillian Byteman allows you to modify bytecode of deployment directly on server, so you don't have to mock but you can force alternative behavior of deployed classes
For instance, here I'm using Arquillian Spock with Arquillian Byteman to change JPA behavior - https://github.com/kpiwko/arquillian-safari/blob/master/arquillian-rest-scenario/src/test/groovy/com/acme/example/test/FaultInjectionSpecification.groovy
For your purpose, I think Warp is the tool you should be looking into - same as Aslak mentioned. Byteman is the most powerful option, but also the most complicated for setup.