Deep breathing, meditation between matches and practice.
Deep breathing is considered the basics of meditation, as the extra oxygen will help keep your heart rate at a more comfortable range. If you find yourself holding your breath during the match when things are tense, you'll want to practice not doing that. You're speeding up your heart rate, which increases agitation.
Meditation can help calm the mind and return you to a neutral state, much like we need to during the match with our characters. I've learned some meditation techniques that with practice I can use in the minute between matches to help calm myself, which as a defensive character is a necessity to keep up with my opponent.
Practice will help, as you'll be more experienced with what can be done against you by the different characters and you'll have less surprises that will startle you. As you become more comfortable with your character and how others approach fighting him/her, you'll be able to keep your calm more when things get tense since the unknown isn't a factor in the tension.
Fighting games aren't just about beating the character on the screen, but has more to do with beating the person that is controlling that character. If you are getting mad, then they are winning. Remember that it is a game, as your mentality going in will also effect how easy it will be to 'ruffle your feathers'.