This theme is very unique in that you can take it over the top, or keep it simple, and both ways are going to read to your guests as Mardi Gras.
With making it a true over the top Mardi Gras themed party, use ornate decorations: all the bright colors (purples, greens, golds), heavy draping in those colors, large ornate centerpieces with masks, table cloths and chair covers that stick to those color schemes, etc. Be bold, and it will definitely scream Mardi Gras!
Or, you can keep it more sophisticated and classy by using the colors as inspiration. PIck one to be your main color (for table linens let’s say) and use another for uplighting around the space. Having each color represent an area in the room instead of mixing all of them together in every element, will take this theme to the “wedding” level. Keep masks simple and white but still ornate in the design, and use bright florals to depict the colors for you. Very classy.