We analyze target detection for sub-Nyquist radar in an environment with clutter. The target is assumed to be a Gaussian point target and the clutter a stationary Gaussian random process. The optimal detector and detection probability under the Neyman-Pearson criterion is derived. We show that the performance loss due to sub-Nyqusit sampling can be very small in the tested examples. When the signal energy remains the same, we compare the detection performance under different sub-Nyquist sampling methods and different transmitted signal bandwidths. After some development of performance metrics with clutter, we also provide the trade-off among the detection performance, the transmitted signal bandwidth, and the number of samples in the clutter-free environment.