The opposition group will boycott next week's ceremony in protest at the matter.
Group Leader Steve Siddons said: “With Council revenues plummeting we keep being told the Cabinet is cutting its cloth to match.
"But once again the whole Council of 50 members, senior officers and the town's 'great and good' have been invited to a free Mayor making bash at the public’s expense.
"The last Labour Mayor, Eric Broadbent, didn’t have this extravagance but still had one of the most successful Mayoral years in the Borough’s history
“It gives the wrong message that we are choosing to cut basic amenities such as closing public toilets but sitting down to feast at the public’s expense. There were pop-up toilets on Royal Albert Drive for the Tour de Yorkshire finish this weekend but for the rest of the year, visitors now have to cross their legs.
“We fully support a leading council member acting as a figurehead for the Council but that does not need to involve unnecessary perks for councillors.
“If the Cabinet do want to spend money on the Mayoralty they could spend some money on training the new Mayor ready for the challenges of the year ahead.
"After a year during which the public has been ejected from Council for the long-held custom of clapping. And instructed to stop, legally permitted, filming of council.
"A year also when councillors at several meetings have not been allowed their right to speak up for their residents the council's credibility needs boosting by the new Mayor.”
At the ceremony next week, Cllr Joe Plant (Con) will replace Cllr Martin Smith (Con) as Mayor.
Cllr Dilys Cluer (Green) will be named Deputy mayor.
A Scarborough Council spokesperson said: "The civic hospitality budget was reduced from Â£9,320 in 2014/15 to Â£3,050 in 2016/17.
"The budget is used for a buffet lunch at the Annual Council meeting for Mayor Making to mark the ceremonial start of each new Mayoral year.
"The same modest budget also has to cover all other civic hospitality throughout the year at significant local events and civic occasions, including the flag flying ceremonies in Armed Forces Week and on Commonwealth Day.”