For US Air Force Staff Sergeant Quincy Garner, a trumpet player with the Band of Liberty stationed at Hanscom Air Force Base, cuts ordered a year ago have a ringing sense of finality. On Tuesday night at Jordan Hall, the band makes its final concert appearance in Boston, and by May, the group will be broken up and its members reassigned to Air Force bands elsewhere in the United States.

Garner and his bandmates toured military bases in Afghanistan last year and have performed at hundreds of events ­annually, from Maine to Manhattan. In 2009, he played taps at Fenway Park to honor Edward M. Kennedy, the late senator. Performing for veterans’ groups, as he has many times in his nine years with the band, has given Garner an appreciation for the emotional bond formed between audiences and the Liberty musicians.

Those who have made the ultimate sacrifice for their country “deserve full honors,” Garner said this week, as he prepared for his band’s final two concerts. The last one will be held Sunday in Worcester.

“When we go someplace like northern Vermont, which doesn’t necessarily have a big military presence, it’s a way to tell vets, ‘Thank you for your service.’ ”

At the free concert at 7 p.m. Tuesday, accompanied by musicians from the New England Conservatory, the Liberty musicians will perform works by Shostakovich, Gershwin, Sousa, and John Williams, among others.

The concerts close the books on an ensemble that has been a New England fixture since 1978, performing at hundreds of events annually, and in a ­variety of configurations, from full concert band to rock and jazz ensembles. Holiday ­parades, family concerts, and veterans’ gatherings have all been on the band’s extensive travel itinerary.

Taking over Liberty’s territorial responsibilities — the band covers the six New England states, plus New York and New Jersey — will be the USAF ­Heritage of America Band, based in Langley, Va., which currently covers a six-state ­region from Pennsylvania to South Carolina.

The realignment is not part of the current sequestration process cutting deeply into the Pentagon budget. Instead, it is the result of a servicewide initiative begun three years ago to trim military bands and their costs. Last March, Liberty was put on notice that it would be dissolved by the middle of 2013.

Several members have ­already been reassigned or ­retired, leaving a core group of 30 musicians, said Captain ­David Alpar, the group’s commander and conductor.

“We’ve already had to curtail the kinds of performances we can mount,” he said, noting the loss of his keyboardist and French horn player.

A dozen years ago, the band had a $600,000 annual budget covering travel and equipment expenses. Its current budget is just $35,000.

Nationwide, the Air Force is deactivating three of its 12 military bands, two of which are stationed overseas. Others are being downsized. In 2010, accord­ing to Pentagon figures, the federal government was paying an estimated $320 million to support 154 military bands, ranging from premier, audition-only units to less elite groups affiliated with National Guard and reserve units.

The yearlong notice has given Liberty “time to say good-bye properly,” as Alpar puts it. The free concert at Worcester’s Mechanics Hall at 3 p.m. Sunday will bring back many of the band’s Liberty alumni for one final musical salute.

Efforts to reverse last year’s order have so far proved fruitless. They include a letter-writing campaign to Massachusetts’s congressmen and US senators and the creation of a Save The Band of Liberty website and Facebook page. Former senator John F. Kerry was the most responsive, campaign ­organizers said. But as Kerry’s focus turned to leading the State Department, they began to lose even that slim hope.

“We’re disappointed, ­because it affects the arts in Boston, and Boston is such an artistically prolific city,” said ­Susan Hagen, who helped lead the campaign. A double bass player on tour with the Boston Pops, Hagen is married to ­Liberty clarinet player, Master Sergeant Kevin ­Connors.

Her personal connection notwithstanding, Hagen said she is worried that phasing out the band, one of the largest units still stationed at Hanscom, could signal the beginning of the end for the air base itself. “It’s scary,” she said. “If Hanscom shuts downs, that has an enormous impact on the local economy.”