Taylor, who some say should never had been on the team, was one of two Crimson Tide players arrested over the weekend. Defensive back Geno Smith was charged with the second DUI, including the second DUI of his Alabama career.
A defiant Saban was unapologetic Monday about choosing to sign Taylor, who was also dismissed from Georgia before signing with Alabama for similar allegations of domestic violence.
"I'm not sorry for giving him an opportunity," Saban said. "I'm sorry for the way things worked out.
"I'm not apologizing for the opportunity that we gave him. I wanted to try to help the guy make it work. It didn't work. We're sorry that it didn't work and we're sorry that there was an incident and we're sorry for the people that were involved in the incident. But we're not apologizing for what we did, and we're going to continue to try to create opportunities in the future."
Kathy Redmond Brown, founder of the National Coalition Against Violent Athletes, said when Alabama signed Taylor in January, she thought it was "a huge mistake" for the message it sent to teammates and to Taylor and because it opens the school up to a Title IX claim.
Saban said on national signing day in February that the lineman "was the kind of guy that deserved a second chance." He said he had spoken to Taylor's high school and junior college coaches, but Georgia's Mark Richt and Athens-Clarke County district attorney Ken Mauldin have indicated that Saban didn't contact them.
"When anybody says, we think this guy deserves a second chance, what qualifies him to say that?" Brown said. "If you're not talking to the prosecutor and you're not talking to the coach, what qualifies him to say what this guy deserves or not?
"And what qualifies as a mistake? If he beat up (Saban's) daughter and grabbed her by the throat, would that be a mistake? That is the crux of the issue."
Saban stopped short Monday of saying he wouldn't recruit another player who had been previously involved in a domestic abuse case. But he added, "We would certainly be very cautious about any player that had any kind of character problem, but especially something like this."
Taylor signed with the Tide months after his dismissal from Georgia and was arrested Saturday. The case in Georgia is still pending.
Saban said Taylor knew he was signed under a "zero tolerance policy." His case has been referred to the university's judicial affairs, according to school spokeswoman Deborah Lane.
The coach said Taylor had been undergoing counselling without missing a session.
"He was in those programs, and it didn't work," Saban said.
Tiffany Carr, interim director of the Alabama Coalition Against Domestic Violence, praised Saban for taking swift action in removing Taylor for the team but said it's not typically a crime committed only once.
"Domestic violence is a learned behaviour, it's a cycle of violence and control," Carr said. "In 21 years, I've never known it to happen just one time."
Taylor has been charged with domestic violence third-degree assault and domestic violence third-degree criminal mischief, Tuscaloosa police said.
The 6-foot-4, 335-pound lineman was dismissed from Georgia in July 2014 following his arrest on aggravated assault and family violence charges for allegedly punching and choking his girlfriend.
It is unclear if the incidents involved the same woman.
Taylor also was among four Georgia football players arrested in March 2014 for receiving double payments for checks of $71.50 issued by the school's athletic department.
He played last season at Copiah-Lincoln Community College in Mississippi.
Saban addressed the team before Monday's practice, talking about Taylor's dismissal and domestic violence.
Though Taylor was signed with a history of domestic violence, centre Ryan Kelly said: "There's a standard that coach Saban and this university hold us to, and that's just something that we don't stand for here."
Alabama athletic director Bill Battle said in a statement Sunday that Taylor had received "extensive efforts to assist him."
"All of us hope that Jonathan and the young lady involved can deal constructively with the issues that led to this situation, and their aftermath, so that both of them can have productive, healthy futures," he said.
A spokesman said Battle was not immediately available for further comment on Monday.
Smith, meanwhile, was arrested on a charge of driving under the influence of alcohol Saturday for the second time in his career. Saban said he would be subject to unspecified disciplinary action but that he didn't consider dismissing him from the team, and he never has for a second offence with drugs or alcohol.
Smith hasn't been allowed to practice this week.
Alabama had also re-signed defensive lineman D.J. Pettway out of a junior college last year, 10 months after the school dismissed him. Pettway was kicked off the team after he and three other Crimson Tide players were charged with robbery in Tuscaloosa, but he apparently has steered clear of further trouble since returning from junior college.
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