The laser-driven ultrafast demagnetization effect is one of the long-standing problems in solid-state physics. The time scale is given not only by the transfer of energy, but also by the transport of angular momentum away from the spin system. Through a double-pulse experiment resembling two-dimensional spectroscopy, we separate the different pathways by their nonlinear properties. We find (a) that the loss of magnetization within 400 fs is not affected by the previous excitations (linear process), and (b) we observe a picosecond demagnetization contribution that is strongly affected by the previous excitations. Our experimental approach is useful not only for studying femtosecond spin dynamics, but can also be adapted to other problems in solid-state dynamics.