Maureen, the average price of an apartment in Manhattan is now $1,130,000 so mansion is not the best term for this tax.

Since the mansion tax does not apply to vacant land, the residential sales transaction can be structured to allocate the purchase price separately between land and the structural home.
Second, the tax only applies to residential property so in a mixed use property the commercial portion is excluded from the calculation.
Finally, but most importantly, despite the fact that the tax applies to home buyers, the parties can contract otherwise so the tax may be apportioned between buyer and seller. It is essential you consult with a lawyer on any questions that have legal components.

That is certainly an interesting tax. I would assume that a lot of property in Manhattan sells for more than $1 million

All properties that sell for $1 million or more in NY State are subject to a 1% of the sale price mansion tax paid by the buyer. More about NYC closing costs below.