GRB 200219A is a short gamma-ray burst (GRB) with an extended emission (EE) lasting $sim 90$s. By analyzing data observed with the {em Swift}/BAT and {em Fermi}/GBM, we find that a cutoff power-law model can adequately fit the spectra of the initial short pulse with $rm E_{p}=1387^{+232}_{-134}$ keV. More interestingly, together with the EE component and early X-ray data, it exhibits plateau emission smoothly connected with a $sim t^{-1}$ segment and followed by an extremely steep decay. The short GRB composed of those three segments is unique in the {em Swift} era and is very difficult to explain with the standard internal/external shock model of a black hole central engine, but could be consistent with the prediction of a magnetar central engine from the merger of an NS binary. We suggest that the plateau emission followed by a $sim t^{-1}$ decay phase is powered by the spin-down of a millisecond magnetar, which loses its rotation energy via GW quadrupole radiation. Then, the abrupt drop decay is caused by the magnetar collapsing into a black hole before switching to EM-dominated emission. This is the first short GRB for which the X-ray emission has such an intriguing feature powered by a magnetar via GW-dominated radiation. If this is the case, one can estimate the physical parameters of a magnetar, the GW signal powered by a magnetar and the merger-nova emission are also discussed.
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