Ridicule, deride, mock, taunt, twit, rally are comparable when they mean to make a person or thing the object of laughter.
Ridicule implies deliberate and often malicious belittling of the person or thing ridiculed.
Deride implies a bitter or contemptuous spirit.
Mock stresses scornful derision and usually implies words or gestures or sometimes acts expressive of one’s defiance or contempt. When used in reference to things, mock often implies a setting at naught that suggests scorn or derision.
Taunt implies both mockery and reproach; it often connotes jeering insults.
Twit may come close to taunt and imply a mocking or cruel casting something up to someone, but twit, like rally, may imply no more than good-natured raillery or friendly ridicule.