Bdellovibrio bacteriovorus are predatory bacteria that burrow into prey bacteria and degrade their cell contents, including DNA and RNA, to grow. Their genome encodes diverse nucleases, some with potential export sequences. Transcriptomic analysis determined two candidate-predicted nuclease genes (bd1244, bd1934) upregulated upon contact with prey, which we hypothesised, may be involved in prey nucleic acid degradation. RT-PCR on total RNA from across the predatory cycle confirmed that the transcription of these genes peaks shortly after prey cell invasion, around the time that prey DNA is being degraded. We deleted bd1244 and bd1934 both singly and together and investigated their role in predation of prey cells and biofilms. Surprisingly, we found that the nuclease-mutant strains could still prey upon planktonic bacteria as efficiently as wild type and still degraded the prey genomic DNA. The Bdellovibrio nuclease mutants were less efficient at (self-) biofilm formation, and surprisingly, they showed enhanced predatory clearance of preformed prey cell biofilms relative to wild-type Bdellovibrio.