No there is not. The ATI Catalyst driver implements OpenCL, which is what GPU miners use to accelerate the SHA256 hashing used in mining. The open source driver does not implement OpenCL. There are experimental projects that aim to implement OpenCL in the open source driver (Clover is an example) - as a Gallium3D state tracker - but so far these only run on the CPU.
GPU drivers are very complex pieces of software. Even if an open source implementation of OpenCL, that runs on the GPU, were to become available, it would likely be orders of magnitude slower than ATI's proprietary implementation, which basically undermines the whole purpose of using the GPU in the first place -- to gain speed.