That's pretty vague.
What is it doing exactly? Is there an error message, does the screen go black, is it a freeze? How do you know it's your GPU that's failing?
You should be able to run Minecraft. The 7470m isn't a great card, it's not horrible, but it's a low end GPU. The second number in the card's name represents the power rating of the card. So the 4 in 7470 indicates what level the card is at in the 7000m series GPUs. 1-4 is low end, 5-6 is mid range, and 7-9 is high end.
Is it just Minecraft? If not, what other games are failing? Do all games fail or is it only certain games? Even if it is all games, specify what they are.
What do you have the graphics settings at for these games? You're not going to run Minecraft at max settings with that card, probably around medium or the high end of low is the best you're going to get.
I've got a desktop with a dual Radeon HD 7970 gpu setup in Xfire, and Minecraft can push those cards pretty hard at the highest settings.
The more information we have, the easier it will be for us to help you troubleshoot the problem. You need to give us a bit more information about exactly what the problem is. You've not given us enough here to even come close to guessing what the problem might be.
Off the top of my head I'd say you're probably trying to run games that your GPU can't handle or with the settings turned up too high. What you have is better than an integrated graphics chip, but it's also still a low end GPU.
