The defendants include members of an eastern Ohio breakaway Amish group. Prosecutors said the attacks were hate crimes.
The defendants said they were internal church disciplinary matters not involving anti-Amish bias.
The defendants, led by Sam Mullet Sr., stood up one by one before U.S. District Court Judge Dan Aaron Polster and said they understand the risks of trial, including lengthy prison terms if convicted.
The judge told one woman she was responding robotically to his questions, and another woman wiped away tears with a tissue as questions were asked of each defendant. Most of the other defendants and their family members in court watched without emotion.
The plea bargains detailed in court would have given many of the defendants sentences of two to three years in prison instead of the possibility of 20 years or more. Several might have been eligible for parole.
Prosecutors say a feud over church discipline led to attacks in which the beards and hair of men and hair of women were cut, an act considered deeply offensive in Amish culture. The Amish believe the Bible instructs women to let their hair grow long and men to grow beards and stop shaving once they marry.
Several members of the group living in Bergholz in eastern Ohio carried out the attacks last September, October and November by forcibly cutting the beards and hair of Amish men and women and then taking photos to shame them, authorities said.
Mullet told The Associated Press in October that he didn't order the hair-cutting but didn't stop his sons and others from carrying it out. He said the goal was to send a message to other Amish that they should be ashamed of themselves for the way they were treating Mullet and his community.
The judge initially said he intended to split the trial in two - with the first trial for Mullet and six others who have been jailed since their arrest. The judge said he was concerned that a trial with 16 defendants might confuse jurors, in part because nine defendants have the last name Miller.
The judge, flipping pages to keep track of the defendants, decided against splitting the trial when the U.S. Marshals Service said it could secure the crowded courtroom. In addition, attorneys expressed concerns about requiring victims to testify twice and adding travel expense for family members to attend two trials.
A prosecutor also raised the issue of whether two juries hearing substantially the same evidence would return with different verdicts.
The defendants in custody appeared in court in jail jump suits with their wrists and ankles cuffed. The men out on bond wore dark slacks with suspenders and blue or white shirts, and the women had blue tops, blue pleated skirts and white kerchiefs tied behind the neck.
Mullet's son, Lester Mullet, 27, who cannot afford to pay an attorney, tried to fire his court-appointed lawyer in court, but the judge said he couldn't do that.
Lester Mullet said he didn't understand why he was locked up pending trial as a possible risk to others when a plea deal with an offer to cooperate might set him free promptly. "It don't make sense," he said.
The other defendants include three other children of Sam Mullet Sr., his son-in-law, three nephews, the spouses of a niece and nephews, and a member of the Mullet community in Bergholz.
Ohio has an estimated Amish population of just under 61,000 - second only to Pennsylvania - with most living in rural counties south and east of Cleveland.