Depends on how paranoid you are.
Technically: Yes, you should be using a different utensil once the meat is cooked. Any contact with raw meat carries a contamination risk, and you can't guarantee the utensil will be heated enough to "cook" it.
If you want to be as safe as possible, reverse the cooking order you're using - stir-fry the veggies first, set them off to the side, then cook the meat, then mix the veggies in again and use a fresh utensil to finish (or wash the current one.) This ensures that the veggies and second utensil only have contact with cooked meat.
Personally? I don't worry about it beyond the obvious - I make sure I rinse the utensil off somewhere in there with some hot (and usually soapy) water, immerse it in the cooking liquid for a bit if applicable, etc. It's not the safest way of going about things, but it strikes a good balance (for me) between risk and convenience. YMMV, obviously.