Spirocyclic compounds containing heterocyclic moieties represent promising 3D scaffolds for modern drug design. In the search for novel anti-flaviviral agents, we have obtained a series of 3-[N,N-bis(sulfonyl)amino]isoxazolines containing spiro-annulated cyclooctane rings and assessed their antiviral activity against tick-borne encephalitis (TBEV), yellow fever (YFV), and West Nile (WNV) viruses. The structural analogs of spirocyclic compounds with a single sulfonyl group or 1,2-annulated cyclooctane ring were also investigated. Almost all the studied 3-[N,N-bis(sulfonyl)amino]isoxazolines revealed antiviral activity against TBEV and WNV. The most active against TBEV was spiro-isoxazoline derivative containing p-nitrophenyl groups in the sulfonyl part (EC50 2.0 ± 0.5 μM), while the highest potency against WNV was found for the compounds with lipophilic substituents in sulfonyl moiety, naphtyl being the most favorable one (EC50 1.3 ± 0.5 μM). In summary, two novel scaffolds of anti-flaviviral agents based on N,N-bis(sulfonyl)amino]isoxazoline were proposed, and the compounds of this type demonstrated activity against TBEV and WNV.