Most of GNU classpath is platform independent, but there is (and has to be) a VM specific layer that handles the behind-the-scenes interactions with the virtual machine and host operating system.
Classpath is not designed to be immediately usable by Java programmers. It requires an appropriate implementation of a number of Classpath VM* classes, etcetera. These classes are normally provided by the target VM's development team.
It should also be noted that some Open Source JVM projects that previously used Classpath are migrating to / have migrated to OpenJDK. One reason is that the Classpath implementation tended to be incompatible with the equivalent Sun JDKs. This is partly due to the 'clean-room' approach taken by the Class-path team (for legal reasons), and partly due to Sun's continuing unwillingness to license the JDK test suites to open source projects. (Apache Harmony has the latter problem too.)