A study of certain symplectic 4-orbifolds with vanishing canonical class is initiated. We show that for any such symplectic 4-orbifold \(X\), there is a canonically constructed symplectic 4-orbifold \(Y\), together with a cyclic orbifold covering \(Y\rightarrow X\), such that \(Y\) has at most isolated Du Val singularities and a trivial orbifold canonical line bundle. The minimal resolution of \(Y\), to be denoted by \(\tilde{Y}\), is a symplectic Calabi-Yau 4-manifold endowed with a natural symplectic finite cyclic action, extending the deck transformations of the orbifold covering \(Y\rightarrow X\). Furthermore, we show that when \(b_1(X)>0\), \(\tilde{Y}\) is a \(T^2\)-bundle over \(T^2\) with symplectic fibers, and when \(b_1(X)=0\), \(\tilde{Y}\) is either an integral homology \(K3\) surface or a rational homology \(T^4\); in the latter case, the singular set of \(X\) is completely classified. To further investigate the topology of \(X\), we introduce a general successive symplectic blowing-down procedure, which may be of independent interest. Under suitable assumptions, the procedure allows us to successively blow down a given symplectic rational 4-manifold to \(\mathbb C\mathbb P^2\), during which process we can canonically transform a given configuration of symplectic surfaces to a ``symplectic arrangement" of pseudoholomorphic curves in \(\mathbb C\mathbb P^2\). The procedure is reversible; by a sequence of successive blowing-ups in the reversing order, one can recover the original configuration of symplectic surfaces up to a smooth isotopy.