Situated across from each other on the color wheel, purple and mint green look vibrant together and make an exciting complementary color combination. Another option is to employ a monochromatic color scheme that involves using darker and lighter shades of one color to create a peaceful feeling.
The analogous color scheme is another interesting combination to use. Find the main color on the color wheel, then choose one or more colors on each side of it to create a lively, yet harmonious look. Mint, being a tint of green, is created by mixing blue, yellow and white. The analogous scheme would include colors which add blue and also colors that add yellow, since they are the root colors of mint. Add gray, black and white to these colors if you wish to create more depth and interest.