Responding to Herald inquiries, Shaw said he had reluctantly accepted Debreceny's resignation.
"Joss has given tireless, loyal support and made an important contribution to the Green cause, and I am deeply grateful for that."
Shaw said Morris-Travers' move out of the chief-of-staff role was to take up a "special projects" role, including providing policy advice on ending poverty in New Zealand.
"We are keen to utilise Deborah's expertise on the rights of children, as well as tapping into her past experience as a member of Parliament," Shaw said.
"Joss and Deborah are superb operators. As these changes are operational issues it would be inappropriate to make any further comment."
The party's support fell 11 points to 4 per cent in the latest One News-Colmar Brunton poll, which came a week after Turei resigned.
A result of less than 5 per cent would mean the Greens would not return to Parliament unless they won an electorate seat, which they have achieved only once in their history.
Tory Whanau has been appointed acting chief of staff.
Morris-Travers was appointed chief of staff in May last year. She was an MP from 1996 to 1999, first with NZ First and then as an independent. She was a minister in the National Party-NZ First coalition.
Debreceny was also appointed in May last year, having previously worked in communications in both the public and private sector.