CRISPR-Cas12a (Cpf1) is a bacterial RNA-guided nuclease that cuts double-stranded DNA (dsDNA) at sites specified by a CRISPR RNA (crRNA) guide. Additional activities have been ascribed to this enzyme in vitro: site-specific (cis) single-stranded DNA (ssDNA) cleavage and indiscriminate (trans) degradation of ssDNA, RNA, and dsDNA after activation by a complementary target. The ability of Cas12a to cleave nucleic acids indiscriminately has been harnessed for many applications, including diagnostics, but it remains unknown if it contributes to bacterial immunity. Here, we provide evidence that cleavage of ssDNA in cis or in trans by Cas12a is insufficient to impact immunity. Using LbCas12a expressed in either Pseudomonas aeruginosa or Escherichia coli, we observed that cleavage of dsDNA targets did not elicit cell death or dormancy, suggesting insignificant levels of collateral damage against host RNA or DNA. Canonical immunity against invasive dsDNA also had no impact on the replicative fitness of co-infecting dsDNA phage, ssDNA phage or plasmid in trans. Lastly, crRNAs complementary to invasive ssDNA did not provide protection, suggesting that ssDNA cleavage does not occur in vivo or is insignificant. Overall, these results suggest that CRISPR-Cas12a immunity predominantly occurs via canonical targeting of dsDNA, and that the other activities do not significantly impact infection outcomes.