Mitotic slippage (MS), the incomplete mitosis that results in a doubled genome in interphase, is a typical response of TP53-mutant tumors resistant to genotoxic therapy. These polyploidized cells display premature senescence and sort the damaged DNA into the cytoplasm. In this study, we explored MS in the MDA-MB-231 cell line treated with doxorubicin (DOX). We found selective release into the cytoplasm of telomere fragments enriched in telomerase reverse transcriptase (hTERT), telomere capping protein TRF2, and DNA double-strand breaks marked by γH2AX, in association with ubiquitin-binding protein SQSTM1/p62. This occurs along with the alternative lengthening of telomeres (ALT) and DNA repair by homologous recombination (HR) in the nuclear promyelocytic leukemia (PML) bodies. The cells in repeated MS cycles activate meiotic genes and display holocentric chromosomes characteristic for inverted meiosis (IM). These giant cells acquire an amoeboid phenotype and finally bud the depolyploidized progeny, restarting the mitotic cycling. We suggest the reversible conversion of the telomerase-driven telomere maintenance into ALT coupled with IM at the sub-telomere breakage sites introduced by meiotic nuclease SPO11. All three MS mechanisms converging at telomeres recapitulate the amoeba-like agamic life-cycle, decreasing the mutagenic load and enabling the recovery of recombined, reduced progeny for return into the mitotic cycle.