"When you have them by the balls, their hearts and minds should/will follow."

This is probably not an ancient saying, since it appears in no on-line searches, including the Perseus Project. It has a very American tone to it, in fact, so I suspect someone rendered the phrase into Latin for your boss. In addition, the use of the first word (actually an adjective meaning "fruitful" or "life-causing") with such a clearly physical noun-meaning is certainly post-classical, and most likely arose only in the past 500 to 1,000 years.

GENITALIBUS CAPTIS: "with the genitals taken, the genitals having been seized." This is an absolute construction in the ablative case, a common circumlocution used in place of a subordinate clause. CAPTIS is a passive-voice participle in the perfect tense, from the verb CAPIO/CAPERE, "take/seize/grasp." Good Latin style avoids overuse of possessive adjectives, so we can add "their" (or others, as appropriate) as needed in English.

CORDA: "hearts." Plural of the neuter noun COR.

MENTESQUE: MENTES: "minds." Plural of the feminine noun MENS. -QUE: "and" in postposition (as a suffix, unlike English!). Latin has several words for "and", including preposed ET, AC, ATQUE, and suffixal -QUE.

SEQUENDA: "to follow" (a gerundive form, not an infinitive), from the verb SEQUOR, SEQUI. The auxiliary verb SUNT ("are") is implicit here. This construction, the gerundive plus "be", normally shows obligation or necessity ("should"), but the tendency of Latin to use very compact, minimalist language certainly permits understanding this phrase merely as a future construction, which was common in mediaeval Latin.