We present the first cosmological measurement derived from a galaxy density field subject to a "clipping" transformation. By enforcing an upper bound on the galaxy number density field in the galaxy and mass assembly survey (GAMA), contributions from the nonlinear processes of virialization and galaxy bias are greatly reduced. This leads to a galaxy power spectrum which is easier to model, without calibration from numerical simulations. We develop a theoretical model for the power spectrum of a clipped field in redshift space, which is exact for the case of anisotropic Gaussian fields. Clipping is found to extend the applicability of the conventional Kaiser prescription by more than a factor of 3 in wave numbers, or a factor of 30 in terms of the number of Fourier modes. By modeling the galaxy power spectrum on scales k < 0.3 hMpc super(-1) and density fluctuations delta sub(g) < 4 we measure the normalized growth rate functionofsigma sub(8) (z = 0.18) = 0.29 + or - 0.10.