Uncontrolled growth in the cell mass of malignant tumors induces intensive angiogenesis. However, the demands of the cancer cells for nutrients and oxygen remain only partially met. Hypoxia is a process that accompanies malignant transformation and evokes changes in the DNA methylation profile in solid tumors. To a certain extent, these changes, including the hypermethylation of tumor suppressor gene promoters, are related to the decrease in the activity of Tet proteins under the conditions of oxygen and free radical deficit. Stabilization, accumulation, and nuclear translocation of the transcription factor HIF1α are the key molecular events in hypoxia. We modified the clear-cell renal cancer cell line Caki1 to stabilize the HIF1α protein and characterized a model cell line that will enable the studies of the mechanisms of changes of the DNA methylation level at a constant activity of Tet proteins and a gene transcription profile characteristic of hypoxia. The CRISPR/Cas9 DNA editing system was used to edit the VHL gene. The mutant VHL protein contained a disrupted alpha-helix at the C-terminus and could not participate in the molecular pathway of proteasomal degradation of the HIF1α factor; therefore, the latter accumulated in the nucleus and activated the specific target genes. An analysis of gene transcription revealed the induction of hypoxia-associated genes in the modified cell line. The developed Сaki-1/VHLmut model can be used to discriminate between the effects evoked by oxygen-suppressed hydroxylases of the Tet family and other hypoxia-associated mechanisms of DNA methylation/demethylation.