His insta heal is big, but only when ally is in his circle. Firstly you and "your allies" should pay attention to "his allies" and them occupy with something. Then when Grover is left alone it's your chance to challenge him on solo fight.
If a Grover is by himself, this can give any champion with decent mobility a chance to close the distance between them and Grover. The closer you get, the more damage you do and the less damage Grover does. Don’t forget about the vine though!
Grover's ultimate does not make him CC immune but stunning him will not cancel the aoe heal. Displacement heavy comps are very powerful against him since they can keep him away from his team and reduce his healing.
Check at the start of the match if Grover has the legendary card which gives him the ability to root with crippling axe, if he does then but the item to reduce CC duration, this can save your life many times during a match.
Unlike most front liners and supports grover has very good long range pressure. He can use his bonus damage scaling legendary to harass enemy front liners from long range or long range enemies from the objective easily.