"夸张地表现感情" can be translated into English as "exaggerate one's emotions" or "display emotions in an exaggerated manner".
Both expressions convey the idea of overdoing or overemphasizing one's emotional reactions. For example:
He tends to exaggerate his emotions when telling stories. （他讲故事时往往会夸张地表现感情。）
She displayed her grief in an exaggerated manner at the funeral. （她在葬礼上夸张地表现了她的悲伤。）