In this work, a new, to the best of our knowledge, model of effective lift-off threshold of an oxide/metal target is presented. The influence of nonlinear processes in the oxide layer on its removal from the metallic samples using a picosecond laser was investigated. Nonlinear and saturable absorption in the layer was incorporated into modeling for prediction of effective laser lift-off threshold fluence change with varying peak intensities in a z-scan-type experiment for the first time. The new model coincides well with the experimental results.