No, grow up would be גדל (pa'al) and מגדל (pi'el) is grow, raise. "grow up" is an intransitive verb, and it can't take an object. The transitive verb in that case is "grow".
הבן שלי גדל.
My son is growing up.
אנחנו מגדלים ירקות בגינה שלנו. We grow vegetables in our garden.
However, you can't use "grow" with animals, only with plants. For animals and children you would use "raise".
אחותי מגדלת את הבת שלה לבד.
My sister is raising her daughter alone.