In this paper, we investigate the arithmetic properties of the coefficients of the eighth-order mock theta function $V_0(q)$, building upon the foundational work of Gordon and McIntosh on mock theta functions. Several novel dissection formulas are derived, leading to new identities for the Dedekind eta function at level 8. Furthermore, we establish new congruence relations and partition recurrence formulas associated with the coefficients of the eighth-order mock theta function.