Master Miyamoto was a teacher at Styrling Academy. He taught swordfighting to numerous students, including Arcturus Mengsk.
Traveling
Mengsk later hired him to teach his son, Valerian, when he had to continually move him around to avoid Confederate agents. Miyamoto taught the child academics and various forms of fighting. He ensured that Valerian learned concepts such as honor. Miyamoto hailed Valerian as his best ever student when it came to using a sword.
Dominion Warrior
Miyamoto accompanied Arcturus and Valerian Mengsk to Umoja six months after the Terran Dominion was inaugurated.
While there, they were struck by a surprise attack launched by the Confederate Resistance Forces. A number of Wraiths and 30 marines led by Captain Angelina Emillian had come to Umoja, seeking to kill Arcturus Mengsk. They heavily outnumbered the Dominion and Umojan defenders.
The Mengsks and Miyamoto took shelter in a landing bay and crashed ship. Miyamoto fought back with his rifle and suffered injuries, eventually falling to a shot in the back from Emillian. Valerian Mengsk and Emillian faced each other, and Emillian clearly had the upper hand... except Miyamoto wasn't dead yet. With his last strength he damaged her gauss rifle with his sword, enabling Valerian to shoot her down.
trivia
Miyamoto's name may be a reference to Shingeru Miyamoto, the founder of Mario and The Legend of Zelda and ultimately, Nintendo
References
McNeill, Graham (December 30, 2008). StarCraft: I, Mengsk. Simon & Schuster (Pocket Star). ISBN 1416-55083-6.