The owners of the dog believed to have killed a miniature horse in Edgartown last weekend have decided to euthanize the dog, while the owner of the horse said she will not press further charges.

Mugsy, a three-year-old neutered American Staffordshire-bulldog cross, will be put down on Monday, animal control officer Barbara Prada said, nine days after two miniature horses were attacked and one killed at an Edgartown farm. The incident rattled residents of the Edgartown neighborhood and highlighted what animal control officers said are rising dog incidents on the Island.

Two miniature horses were attacked at a Meetinghouse Way Farm owned by Ellen Harley sometime between 11 a.m. and 4:30 p.m. Saturday afternoon, Mrs. Prada said. Mrs. Harley’s horse Magik was killed, while Chance, owned by Kirsten Davey, was injured but recovered.

Mugsy, owned by Adam Mahoney, was placed on 10-day quarantine at the pound, and Mr. Mahoney’s other dog that was believed to be loose Saturday, a four-year-old neutered pointer cross, was placed in quarantine at home. Ms. Prada said she does not believe the second dog was involved, noting that she didn’t think he was capable of jumping over the fence.

Ms. Prada said Mr. Mahoney visited Mugsy at the pound Monday afternoon and “agreed they had to do the right thing and put Mugsy down,” she told the Edgartown selectmen this week.

She said the dog would be euthanized after the 10-day state mandated quarantine is over on Monday, and the owners would arrange for a veterinary appointment either at their home or a clinic.

The Edgartown selectmen said they wanted to be sure the dog remained in quarantine or under the town’s control, and they voted 3-0 that the dog was dangerous and should not be released unless to the owner for euthanasia.

Ms. Prada’s assistant, Jamie Pience-Riley, was on duty and called her when she received the report about the incident late Saturday afternoon. A woman who had been feeding and caring for the horses found a gruesome scene in the paddock with one miniature horse dead and another injured.

Ms. Prada said the animal that killed the horse cleared a four-foot split-rail fence that was lined with sheep fencing and was intact. She said there was no evidence that the horses had been chased or dragged down. Two other full-sized horses nearby were unharmed, she said.

“There were no bite marks on the horse [that was killed], the dog went right for the jugular, telling me the dog had done something like this before. It has to be a good-sized dog, or possibly dogs,” Ms. Prada said early Sunday. She said the horse that was killed had most of its face ripped off. The injured horse had puncture wounds, was treated on the scene by its owner and was recovering at the farm Sunday.

There were no known witnesses to the incident.

Ms. Prada said by protocol she called an Edgartown police officer and the chairman of the board of selectmen to the scene as witnesses. Board chairman Margaret Serpa and Edgartown police officer William Bishop responded.

“Honestly, it was probably the most horrific animal complaint call I have responded to,” Officer Bishop said Sunday morning.

Farm owners in the Meetinghouse Way area, a rural area on the outskirts of Edgartown that reaches down to the Edgartown Great Pond, were notified to be extra vigilant in minding their livestock.

Ms. Prada said a tip led the Edgartown police department to the dog owned by Mr. Mahoney, who lives in Island Grove. The Mahoneys confirmed that Mugsy had been on the loose Saturday and had returned home bloody, muddy and covered with scratches. Ms. Prada said the owners cooperated fully with the police and animal control department. “The owners feel terrible and they had no idea,” Ms. Prada said.

“I sort of thought of Mugsy at the time, but without proof didn’t want to go and accuse people,” Ms. Prada told the selectmen, noting that the dog had bitten a calf at Morning Glory Farm a year and a half ago.

Before Mugsy was found, there was some speculation about whether a coyote was responsible. Ms. Prada thought this was highly unlikely, and Augustus (Gus) Ben David 2nd of Edgartown, a noted Vineyard authority on wildlife biology who has carefully tracked a small handful of coyote sightings on the Vineyard in the past two years, concurred.

“I can tell you on very firm biological grounds that this is not a coyote kill,” Mr. Ben David said Sunday morning. “We haven’t had a reliable coyote sighting in well over a year, and this is an atypical situation. If we did have coyotes here, at this time of year there is a plethora of wildlife for them to eat,” he said. He also noted that the small handful of sightings were on the remote north shore area of the Island. “We have never had a sighting down-Island,” Mr. Ben David said.

Mrs. Harley, who divides her time between South Carolina and Edgartown, said Wednesday that she was not going to take any further action, saying all involved have suffered enough. “I think the people have made an incredibly difficult decision,” she said. “I don’t think anybody wins in this situation. I applaud them for stepping up and doing the right thing.”

“Of course, we’re devastated still by what happened,” she said. “The decision they are making is the right decision for everyone.”

She said the incident was traumatic for those who work at the farm, but “we’ve all committed to just moving forward now.” She arrived on the Island this week to stay until November.

She added that she wanted to “thank Barbara Prada and the police department for just moving so quickly and so efficiently to bring this dog to justice for the whole community.”

Ms. Prada, who is in her 31st year as animal control officer, said that she’s “definitely seen an increase” in incidents involving dogs.

According to the 2012 animal control report, there were 865 dog calls in 2012, with 13 dog bites reported, and 105 leash law violation tickets issued. The town also has a high number of farm animals, including 1,629 poultry.

“I kind of chalk it up to the fact that some people don’t necessarily train their dogs very well,” Ms. Prada said. “Some people don’t really train their dogs well, some people are getting dogs when they really don’t know the dog well and don’t know what they’re getting.”

“They are animals,” she added. “Some dogs have stronger instincts than others.”

The best thing an owner can do, she said, is follow the leash law and keep his or her dog restrained.

Tisbury animal control officer Laurie Clements said the increase in dog biting incidents is “just ridiculous.”

“I don’t know what’s going on,” she said. “There seems to be an awful lot of dog bites,” noting that dogs are biting kids and people and other dogs. Just last weekend, she said, there were two incidents: one dog that bit another dog and another that bit a person. The dogs are in quarantine at their homes, and “the owners are both very remorseful.”

She concurred that the leash law is the most important deterrent. “That’s the best way to keep your dog and yourself out of trouble and the public protected.”

She also noted that there are more pit bulls and American bulldogs on the Island, though she cautioned that she’s not saying those are the main culprits. “It seems to be a lot of those dogs that are doing the biting.”

Ms. Prada said she was asked if she would put the dog down if it was hers. “In a heartbeat,” she said. “If my dog bit some kid or anybody or attacked an animal, that’s it, my dog’s number is up.”