Many studies have shown that either the nearby astrophysical source or dark matter (DM) annihilation/decay is required to explain the origin of high energy cosmic ray (CR) $e^pm$, which are measured by many experiments, such as PAMELA and AMS-02. Recently, the Dark Matter Particle Explorer (DAMPE) collaboration has reported its first result of the total CR $e^pm$ spectrum from $25 ,mathrm{GeV}$ to $4.6 ,mathrm{TeV}$ with high precision. In this work, we study the DM annihilation and pulsar interpretations of the DAMPE high energy $e^pm$ spectrum. In the DM scenario, the leptonic annihilation channels to $tau^+tau^-$, $4mu$, $4tau$, and mixed charged lepton final states can well fit the DAMPE result, while the $mu^+mu^-$ channel has been excluded. In addition, we find that the mixed charged leptons channel would lead to a sharp drop at $sim$ $mathrm{TeV}$. However, these DM explanations are almost excluded by the observations of gamma-ray and CMB, unless some complicated DM models are introduced. In the pulsar scenario, we analyze 21 nearby known pulsars and assume that one of them is the primary source of high energy CR $e^pm$.Considering the constraint from the Fermi-LAT observation of the $e^pm$ anisotropy, we find that two pulsars are possible to explain the DAMPE data. Our results show that it is difficult to distinguish between the DM annihilation and single pulsar explanations of high energy $e^pm$ with the current DAMPE result.
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