"以贬抑的口吻" can be translated into English as "in a derogatory tone" or "with a condescending/derogatory manner of speaking".
Here are some example sentences for context:
1、 He spoke in a derogatory tone, making others feel uncomfortable.
(他以贬抑的口吻说话,让别人感到不舒服。)
2、 She criticized him with a condescending manner, which was quite offensive.
(她以贬抑的口吻批评他,这相当冒犯人。)