The 5′,8-cyclo-2′-deoxypurines (cdPus) affect the DNA structure. When these bulky structures are a part of clustered DNA lesions (CDL), they affect the repair of the other lesions within the cluster. Mitochondria are crucial for cell survival and have their own genome, hence, are highly interesting in the context of CDL repair. However, no studies are exploring this topic. Here, the initial stages of mitochondrial base excision repair (mtBER) were considered—the strand incision and elongation. The repair of a single lesion (apurinic site (AP site)) accompanying the cdPu within the double-stranded CDL has been investigated for the first time. The type of cdPu, its diastereomeric form, and the interlesion distance were taken into consideration. For these studies, the established experimental model of short oligonucleotides (containing AP sites located ≤7 base pairs to the cdPu in both directions) and mitochondrial extracts of the xrs5 cells were used. The obtained results have shown that the presence of cdPus influenced the processing of an AP site within the CDL. Levels of strand incision and elongation were higher for oligos containing RcdA and ScdG than for those with ScdA and RcdG. Investigated stages of mtBER were more efficient for DNA containing AP sites located on 5′-end side of cdPu than on its 3′-end side. In conclusion, the presence of cdPus in mtDNA structure may affect mtBER (processing the second mutagenic lesion within the CDL). As impaired repair processes may lead to serious biological consequences, further studies concerning the mitochondrial repair of CDL are highly demanded.