In the months leading up to his meeting with undisputed world middleweight champ Marvelous Marvin Hagler, John (The Beast) Mugabi repeatedly told his manager, "I'm going to beat my daddy. I'm going to nuke 'im out."

His daddy, in this case, was 160 pounds of bald meanness, a man with a stubborn chin, hands like thunder and a spirit so large one wondered how his body could contain it. Hagler, making his 12th defense since he won the title almost six years ago, beat the previously undefeated Ugandan on Monday night before more than 15,000 in an outdoor arena at Caesars Palace, winning the bout with a stunning, 11th-round knockout.

Hagler, whose record stands at 62-2-2, started slowly, switching from a right-handed boxing style to a southpaw pose while trying to overcome the challenger's awkward counter-punching approach. In the fourth, Mugabi scored with a quick right uppercut that popped the champion squarely on the chin but apparently did not rattle him. The middle rounds were spectacular, particularly the sixth, when Hagler let go his level best and still was unable to topple Mugabi.

In that round, Hagler threw 95 punches, landing 59. In comparison, the champion threw 82 in the first round of his celebrated April 15, 1985, bout with Thomas Hearns. As Hagler flailed away at Mugabi, moving him against the ropes and working hands sharply into his head and body, wisps of steam rolled off the bodies of both men and sweat and blood spit to the canvas floor. Hagler had hurt the challenger. After the fight, he said he thought referee Mills Lane should have stopped the scheduled 12-round bout to prevent serious injury to Mugabi.

The fight ended at 1:29 of the 11th round, after Hagler charged the weary Mugabi and blasted him twice with rights. At that point, Hagler's right eye was almost swollen shut and he spit blood from a cut inside his mouth. One good punch to the temple might have burst the champion's hematoma wide open, but Mugabi was too tired to do anything but work for survival. A silver medalist in the 1980 Olympics at Moscow, Mugabi had won all 26 of his previous professional fights by knockout, primarily using wild, hitching right hands that came storming out of nowhere.

By the 11th, Mugabi's right was a silent, stony paw pecking at the bright air, rarely touching the champion. When Mugabi fell, he sat up at the count of seven and looked at the world that screamed and whirled before him. Hagler hustled to a neutral corner, raised his hands and rejoiced, shouting, "I came to dinner! I feasted on The Beast!" More than $2 million richer, Hagler now needs only two wins to tie Carlos Monzon's middleweight record of 14 consecutive title defenses.

Goody Petronelli, Hagler's trainer, said, "Our plan in the 11th was to wait until Mugabi made a mistake and then take advantage. Mugabi is not a long-distance fighter. We saw that he was slowing down. Marvin had enough in him to come up with the strong finish. When Mugabi slowed way down, Marvin just took it to him and made it pay off."

After appearing on a morning television show, Hagler did not show up at the postfight news conference today, choosing instead to remain in his hotel suite and sleep. His manager, Pat Petronelli, said that Hagler was in no mood to answer questions about future opponents and that he definitely would not fight Hearns in a June 23 rematch, as had been reported. He said a fight in late November was more likely.

"Right now," Pat Petronelli said, "Marvin wants to get away to Hawaii for three weeks with his family and relax and get his mind off things . . . . He just needs some time to himself."

Hagler, 31, has been mumbling about retiring since he beat Wilford Scypion in Providence in May 1983. But Goody Petronelli said the champion probably would not quit fighting until the summer of 1987, when he hopes to break Monzon's record. He said the Mugabi fight was one of the three toughest defenses Hagler has had since winning the crown in 1980. He said the other two most difficult fights were against Hearns and Juan Roldan in March 1984.

"Mugabi never really hurt him, but his body was sore," Goody Petronelli said. "It's always difficult with counter punchers. If you don't punch, you don't fight. You have to take the lead, and they're setting up to punch your lights out when you come in."

No one had time to fall asleep during the fight that preceded Hagler-Mugabi. To win the North American Boxing Federation middleweight crown, Hearns sent a flurry to the body of James Shuler, knocking the wind clean out of his lungs. Hearns then dropped Shuler with a pair of right hands and claimed the knockout victory at 1:13 of the first round. Afterward, Hearns said, "I want the rematch with Hagler very badly because there's never a day, a time, a minute throughout the day that I don't think about it. Being here and being in training for the last seven weeks has been very difficult, because I had to take Hagler off my mind and concentrate on James Shuler."