CRISPR-Cas13 systems are unique among Class II CRISPR systems, as they exclusively target RNA. In vitro and in prokaryotic cells, Cas13 cleaves both target and non-target RNA indiscriminately upon activation by a specific target RNA. This property has been exploited for development of diagnostic nucleic acid detection tools. In eukaryotic cells, CRISPR-Cas13 initially seemed to exclusively cleave the target RNA and consequently, CRISPR-Cas13 has been adopted as a specific RNA knockdown tool. Recently, several groups have reported unexpected toxicity or collateral cleavage when using CRISPR-Cas13 in eukaryotic cells, which seems difficult to reconcile with the reported target specificity. To understand these seemingly contradicting findings, we explored the collateral cleavage activity of six Cas13 systems, and show that only the most active ortholog in vitro, LbuCas13a, exhibits strong collateral RNA cleavage activity in human cells. LbuCas13a displayed collateral cleavage in all tested cell lines, targeting both exogenous and endogenous transcripts and using different RNP delivery methods. Using Nanopore sequencing, we found that cytoplasmic RNAs are cleaved without bias by LbuCas13a. Furthermore, the cleavage sites are highly specific and often present in Uracil containing single stranded RNA loops of stem-loop structures. In response to collateral RNA cleavage, cells upregulate stress and innate immune response genes and depending on target transcript levels, RNA degradation resulted in apoptotic cell death. We demonstrate that LbuCas13a can serve as a cell selection tool, killing cells in a target RNA specific manner. As such, CRISPR-Cas13 is a promising new technology that might be useful in anti-tumor applications.