When taking cuttings from a plant, I try not to take more than 1/3 of the current healthy growth. For some plants, you shouldn't take even that much. As has been mentioned, mint is very prolific and a fast grower, so you should be just fine taking around 1/3 of the currently growing, healthy young branches each time you cut.
Also, mint can be propagated from the roots. After your plant has become well established, remove it from its pot and look for thick, pale root-like stems lying just under the soil surface. Many of these will have growing tips already starting to come out of the jointed areas. Carefully cut a few of these roots from the mother plant, then cut them into 2-4 inch pieces, and place them horizontally just under the surface of a flat or pot of moist soil. Give them a bit of time to send out new growth before transplanting them into their own pots. Most of them should "take" and this will enable you to get your mint propagated out just a bit faster.