Large-scale process fluctuations (particularly random device mismatches) at nanoscale technologies bring about high-dimensional strongly nonlinear performance variations that cannot be accurately captured by linear or quadratic response surface models. In this paper, we propose a novel projection-based piecewise linear modeling technique, P2M, to address such a modeling challenge with affordable computational cost. P2M borrows the projection pursuit idea from mathematics to convert a high-dimensional modeling problem to a low-dimensional one. In addition, a new piecewise-linear model template is proposed and tuned for strongly nonlinear performance variations. By exploring the unique piecewise-linear nature of the model template, a robust numerical algorithm is further developed to determine all model coefficients by solving a sequence of over-determined linear equations. Several circuit examples designed in a commercial 65nm CMOS process demonstrate that compared with the traditional quadratic modeling, P2M achieves 2x error reduction with neglectable computational overhead.