It is right.
简析：Tom (with his mother) often goes to the zoo on Saturdays.
不看括号里的内容.主语Tom,谓语goes,宾语the zoo,时间状语 on Saturdays
已经是完整的句子了.
那再看括号里的内容,with his mother只是作介词短语,其实整句的真正主语是Tom.所 以谓语动词用三单形式.
你也可以将介词短语置于后面,如：Tom often goes to the zoo with his mother on Saturdays.这样你就很清楚为什么谓语动词用的goes了.