I assume you are talking about a Black/Red Vampire Standard deck with Curse of Stalked Prey as the card that generates the counters.
Hex Parasite is probably a bad idea, as it will completely hog your mana supply. You have to pay mana to remove counters which he put on basically for free. You may be able to eat the counters, but the creatures will still hurt you with their base power and you will be unable to cast anything significant for additional defense. Since you are talking about a G/R deck, you won't have a lot of black mana available either, so you typically pay life (Phyrexian mana) to reduce damage - so Hex Parasite is not only mana-intensive, it doesn't even save you any life loss. Hex Parasite is clearly an offensive utility creature, not defensive.
A much better strategy is to simply beat down on your opponent better than he does, or to attack Curse of the Stalked Prey or the creatures themselves, without which the Curse is useless. With Green/Red, you should be able to pursue both strategies efficiently.
Green is known for being able to handle enchantments, and red is good at destroying lots of small creatures with damage.
So basically your strategy is to never let the enemy attacks gain any momentum. Put out some creatures of your own, especially green ones, which should be more efficient ( = more power/toughness per cost) than your opponent's black and red ones. If he manages to build a large army because of a stalemate, create card advantage by sweeping the board clear of creatures with your red spells (card advantage: you have more cards in hand and battlefield combined than your opponent). If you just want to go for a straight damage race, just make sure you get rid of the Curses with enchantment destruction.