  In this paper, we define the affine super Yangian
$Y_{\varepsilon_1,\varepsilon_2}(\widehat{\mathfrak{sl}}(m|n))$ with a
coproduct structure. We also obtain an evaluation homomorphism, that is, an
algebra homomorphism from
$Y_{\varepsilon_1,\varepsilon_2}(\widehat{\mathfrak{sl}}(m|n))$ to the
completion of the universal enveloping algebra of
$\widehat{\mathfrak{gl}}(m|n)$.
