I don't understand. Are you saying you want to use a Home Equity Loan or a cash out mortgage to finance your new build?
If so, I am pretty sure that is a resounding no.

Absolutely not - your house goes away in the process so the collateral goes away. If the build stopped after the house was torn down and all the permits were paid for and lot cleared, the bank would be left holding the note. They don't like that possibility.

"They don't like that possibility."

It is usually prohibited on the note.

It would fall under 'wasting' (at least).

We are doing sort of what you describe - we basically took the house down to the studs for the part that we want to preserve (about 950 sq ft), demolish other sections, then put down a new foundation for the remaining 2400 sq ft. It is essentially a new build.

We were able to secure a construction loan. Basically, the bank will buy out your existing loan, and then look at the cost of construction, and what your finished home will be worth... they will loan an amount that is a percentage of that - 75% LTV. In our case, we were able to meet the requirements and got the loan, although they made us jump through a lot of hoops.

You would need to have substantial equity in the property and the proposed new structure would need to be able to meet a high enough appraisal figure for any bank to even talk to you about this. In other words, if this is a tiny old home on an estate sized lot surrounded by estate sized homes, and it's almost paid off, then you probably could be financed for that million dollar build if your income met the guidelines for the new loan amount. Even then, you'd better have substantial cash reserves in case it doesn't make the appraisal.