From the Super Mario Wiki
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During Mario's first visit to the Mushroom Kingdom, Raz tells the plumber about his engagement to Raini and that they are planning their wedding. Unfortunately, as the two lovebirds are planning, the villain Mack invades the Mushroom Kingdom, effectively postponing the wedding. After Mario and Mallow liberate the peaceful kingdom, Raz and Raini decide to be wed in Marrymore, the marriage capital of the world.
However, misfortune befalls the couple again. During their wedding in Marrymore, a maniac named Booster arrives and kicks everyone out of the chapel so he can get married to the kidnapped Princess Peach. Ultimately, Mario stops Booster's mad wedding, saves the princess, and reopens the chapel so Raz and Raini can (finally) get married.
Raz is unable to ride Yoshi. It is not clear exactly what prevents him from doing this, although it is somewhat implied that he does not know how.
Raz is last seen with Raini in the ending sequence of the game.