In this paper, we first introduce a grand mixed generalized Morrey spaces $M^{P),\Psi(\cdot)}*{u}(\mathbb{R}^{n})$, where $P=(p*{1},\cdots,p_{n})\in(1,\infty)^{n}$, $\Psi(\cdot)=(\psi_{1}(\cdot),\cdots,\psi_{n}(\cdot))$ is $n$-tuple of positive increasing functions $\psi_{i}$ defined on intervals $(0,p_{i}-1]$ for $i=1,\cdots,n$, and\$u(X,r): \mathbb{R}^{n}\times(0,\infty)\rightarrow(0,\infty)$ is a Lebesgue measurable function; especially, if we take $\Psi(\Upsilon):=\Upsilon^{\Theta}$ with $0<\Upsilon:=(\varepsilon_{1},\cdots,\varepsilon_{n})<P-1$ and $\Theta:=(\theta_{1},\cdots,\theta_{n})>0$, then the space $M^{P),\Psi(\cdot)}*{u}(\mathbb{R}^{n})$ is denoted by $M^{P),\Theta}*{u}(\mathbb{R}^{n})$. Furthermore, we establish the embeddingand density properties for the spaces $M^{P),\Psi(\cdot)}*{u}(\mathbb{R}^{n})$. Finally, as some applications, we prove that a bilinear $\omega$-type Calder'{o}n-Zygmund operator$\widetilde{T}*{\omega}$ is bounded from the product of spaces $M^{P_{1}),\Theta}*{u*{1}}(\mathbb{R}^{n})\times M^{P_{2}),\Theta}*{u*{2}}(\mathbb{R}^{n})$ into spaces $M^{P),\Theta}*{u}(\mathbb{R}^{n})$; and also show that the commutator $\widetilde{T}*{\omega,b_{1},b_{2}}$ generated by $b_{1},b_{2}\in\mathrm{BMO}(\mathbb{R}^{n})$ and $\widetilde{T}*{\omega}$ is bounded from\ the product of spaces $M^{P*{1}),\Theta}*{u*{1}}(\mathbb{R}^{n})\times M^{P_{2}),\Theta}*{u*{2}}(\mathbb{R}^{n})$ into spaces $M^{P),\Theta}*{u}(\mathbb{R}^{n})$, where $u*{1}u_{2}=u$ and $1<P_{1}, P_{2}<\infty$.Moreover, the boundedness of $\widetilde{T}*{\omega}$ and $\widetilde{T}*{\omega,b_{1},b_{2}}$ on the product of grand mixed Morrey spaces$M^{P_{1}),\Theta}*{q*{1}}(\mathbb{R}^{n})\times M^{P_{2}),\Theta}*{q*{2}}(\mathbb{R}^{n})$ is established.