As a martial artist, an instructor, a former law enforcement individual, and a fan of star wars galaxy, I am going to try to answer this question. However, I am not claiming to be an expert on any one subject, especially martial arts OR mandalorian history/culture. So, before you send me a msg about how wrong I am,.. please understand that I mean from the bottom of my heart,.. "get over it."
There is no established martial arts system originating from Mando culture. However, as a historical fighting race with specialties in mercenary, bounty, and security work, its almost a given that there WOULD be a mando martial art. The mandalorians were far too thorough and realistic to assume that their weapons and technology would always be enough to win the battle.
So, now the question is "What type of martial art would evolve in a mandalore culture?". NovallTalon really did a good job of hitting the nail on the head. Mandalorians wouldn’t want a flowery martial art, similar to wushu or modern tae kwon do. Though both arts have their own legitimate advantages and ARE useful in a warfare or streetfight situation, they are very difficult styles to master. The years of training required to throw, flip, kick, and punch rapidly with the grace and speed of flashier martial arts, while still generating credible power, would be too long and too tedious to be accepted by the mandalorian mind set.
An style like Krav Maga is much more straight forward. It is about gross motor reflexes. Throwing elbows, knees, head butts. Guttural, brutal power moves that devastate an opponent rapidly. Imagine receiving any one of those strikes, delivered from a heavily armed attacker! ouch. Eye gouges, groin strikes, small joint manipulation, and other "illegal" moves are all a part of this style. Knife and gun defenses are also addressed in Krav Maga. Also, after a mandalorian soldier developed a basic mastery of a straight forward, no frills style like Krav Maga, he could accent his arsenal of hand-to-hand techniques with more advanced and more complex maneuvers.
For example, as a bounty hunter or bodyguard, "custody and control" geared martial arts would be a high priority to have a basic understanding of. Brazilian Jujitsu, small circle jujitsu, chin na kung fu, aikido, and any law enforcement used style would all fall in this category. These styles would involve the kind of techniques required to take an opponent down without killing or damaging them too much. Wrist locks and rear naked chokes fall in this category.
We'll assume a mandalorian would never assume his hand-to-hand skills are perfect and constantly strive to gain more knowledge to supplement his techniques. This means even more advanced techniques. Jump kicks, flips, edged weapons, improvised weapons, etc would all fall into this category. This is where the variety and the personal preferences begin to show. A long legged mandalorian would probably learn to kick. A mandalorian with a muscular build and a penchant for down and dirty fighting might learn how to grapple.
So,.. to break it down: ASSUMING there was a mandalorian martial art, it would MAYBE be geared to fit the needs of a its users.
First: a style like Krav Maga would be a good start to develop the skills to defend oneself and eliminate the enemy.
Second: Jujitsu, aikido, or any other law enforcement style would give an aspiring bounty hunter more skills to be used "on the job".
Third: After gaining a basic mastery of required skills, a mandalorian would develop a more personal, taylor made style of combat to suit them better.
AND: mastery of weapons is a martial art, with each device requiring its own style and skills to learn. GUN-FU if you will. kali, escrima, etc are all styles you should look into.
AND AGAIN: mandalorians lived in a galaxy with very different species with a wide variety of biological traits. IF a true mandalore style existed, it would have specialized techniques used for certain species and certain species only.
sooo,.. its all very complex. I probably was more confusing than helpful. LOL.