Saward, who is understood to be sailing in Europe, was unable to be contacted last night.
It is believed the team will hold a crisis meeting at its Viaduct Harbour base today to address the departures and plot the way forward, with the first event on the America's Cup World Series circuit now less than six weeks away.
"Nick Holroyd has resigned from Emirates Team New Zealand. However ETNZ does not wish to comment on personnel issues at this stage," a Team New Zealand statement said.
"We remain on track to mount a competitive challenge for the 35th Americas Cup and Grant Dalton is currently in Europe pursuing some very exciting opportunities for the team."
The latest departures come after former skipper Dean Barker walked away in February after a very public employment dispute. Chairman Keith Turner then resigned in April after just over a year in the position.
Barker will likely be watching the latest developments at his old team as he looks to assemble a strong and experienced crew for the new Japanese challenge he is heading up.
Holroyd, in particular, is a major loss for Team NZ. The naval architect and engineer has been with the syndicate since 1997, and led the design effort for the last campaign, during which the team made the leap from monohulls to high-performance foiling catamarans.
He will take with him out the door a wealth of intellectual property from nearly two decades with the team, including its design secrets from the last America's Cup.
The learnings from the 2013 series in San Francisco, which was sailed in giant AC72 wingsailed catamarans, will be transferable to the next event in Bermuda in 2017, which will be sailed in smaller 48-foot catamarans.
It is likely Holroyd will have strict restraints of trade imposed that may prevent him joining another team.
The latest departures cap off a tumultuous six months for Team NZ, who were forced to let go several long-serving members of the team late last year following a major restructure as part of cost-cutting.
The most high-profile casualty of that restructure was Barker, who was ousted from the sailing team and offered a performance-analyst role, which he turned down following a messy falling-out with team boss Grant Dalton.