There is no Mayfair-specific exemption, and Saskatchewan has no land transfer tax for a relocating buyer to budget for either, so the real moving costs are the Information Services Corporation title transfer fee, legal fees of $800 to $1,500, and a home inspection at $400 to $600 given Mayfair's older housing stock.
The mill rate applied to your assessed value is set annually by the City and by the school divisions, and it is the same rate whether the home sits in Mayfair or across the river, so what changes your bill is your home's assessed value, not its neighbourhood name.
Getting the assessed value right before you close, especially on an older Mayfair home with past renovations, is worth checking against a real valuation rather than the notice alone. Get your hand-reviewed valuation from Joel Dyck.