Modern decompilers generally produce a reasonably high-quality output, which, after minor modifications, can be read and debugged as any usual Java source code. There are multiple IDEs supporting Java that provide debugging options for this purpose: Eclipse, NetBeans, Intellij IDEA, and others.
In case the original bytecode stream tracing is required, it is possible to achieve this with the -XX:+TraceBytecodes option that's available for debug builds of the HotSpot JVM. If step-by-step bytecode debugging is required, then Dr. Garbage's Bytecode Visualizer plugin for Eclipse IDE appears to be extremely handy. It allows you to not only see the disassembly of the compiled modules inside the JAR, but also the ability to debug them.