Biological process

down regulation of cytotoxic T cell differentiation, down-regulation of cytotoxic T cell differentiation, downregulation of cytotoxic T cell differentiation, negative regulation of cytotoxic T lymphocyte differentiation, negative regulation of cytotoxic T-cell differentiation, negative regulation of cytotoxic T-lymphocyte differentiation

Any process that stops, prevents, or reduces the frequency, rate or extent of cytotoxic T cell differentiation.

negative regulation of cytotoxic T cell development

Note that immunologists typically use the word 'development' to refer to cells of B or T cell lineages undergoing the process that GO describes as 'cell differentiation'.