Biogas digesters are commonly used to treat animal manure/slurry, and abundant digested slurry is generated during the digestion process. Gas emissions from digested and raw slurry may vary with the change in slurry parameters after digestion, but the mechanism is not well understood. Gas emissions from raw dairy slurry (RS) and digested dairy slurry (BS) during 98 days of storage were investigated in this study to evaluate the effects of anaerobic digestion on reactive nitrogen emissions from slurry storage. Results showed that much higher N2O and NO emission and lower NH3 emission was achieved in BS than in RS. The mean gaseous emission of RS and BS accounted for 27.8% ± 6.9% and 17.1% ± 2.3% of the initial TN for NH3, 0.1% ± 0.1% and 3.5% ± 1.6% of the initial TN for N2O, and 0.0% ± 0.0% and 0.2% ± 0.0% of the initial TN for NO, respectively. Among all detected N2O-forming and reducing microbial genes, the abundance of amoA genes was the most closely related to N2O flux (r = 0.54, p < 0.01). More aerobic conditions occurred in BS, and dissolved oxygen (DO) increased to 0.4–1.6 mg L−1 after 35 days because the low organic matter of BS resulted in good infiltration of surface air into the slurry. The increased DO stimulated the growth of Nitrosomonas and the increase in amoA gene copies and contributed to the high N2O and NO emissions in BS through the nitrification process. Vulcanibacillus, Thauera, Castellaniella, and Thermomonas were the major denitrifying bacteria that occurred in BS and caused an incomplete denitrification process, which could be another reason for the increase in N2O and NO emissions from BS. Our study indicated that anaerobic digestion reduced the organic matter content of the slurry and caused an active microbial environment that facilitated the transformation of slurry N to N2O in BS storage, thus lowering the NH3 emission compared with RS storage. Therefore, aside from NH3, N2O should also be preferentially mitigated during BS storage because N2O is a greenhouse gas with high global warming potential.