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In this paper, it is proved that if $b_{1},b_{2}\\in {\\rm CMO}$ (the {\\rm BMO}-closure of $C^{\\infty}_{c}(\\mathbb{R}^n)$), $[\\Pi \\vec{b},T]$ and $[\\Pi\\vec{b},I_{\\alpha}]$ $(\\vec{b}=(b_{1},b_{2}))$ are all the compact operators from $\\mathcal{M}^{p_{0}}_{\\vec{P}}$ (the norm of $\\mathcal{M}^{p_{0}}_{\\vec{P}}$ is strictly smaller than $2-$fold product of the Morrey norms) to $M^{q_{0}}_{q}$ for some suitable indexes $p_{0},p_{1},p_{2}$ and $q_{0},q$. 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In this paper, it is proved that if $b_{1},b_{2}\\in {\\rm CMO}$ (the {\\rm BMO}-closure of $C^{\\infty}_{c}(\\mathbb{R}^n)$), $[\\Pi \\vec{b},T]$ and $[\\Pi\\vec{b},I_{\\alpha}]$ $(\\vec{b}=(b_{1},b_{2}))$ are all the compact operators from $\\mathcal{M}^{p_{0}}_{\\vec{P}}$ (the norm of $\\mathcal{M}^{p_{0}}_{\\vec{P}}$ is strictly smaller than $2-$fold product of the Morrey norms) to $M^{q_{0}}_{q}$ for some suitable indexes $p_{0},p_{1},p_{2}$ and $q_{0},q$. 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