I think your problem is, that when copying/cutting and pasting the cell, all cell references will be to old sheet - i.e. you get formulas with links to old workbook. I'm right?

When copying the formula into another workbook, I select the source cell, and copy the formula from formula bar. After that I activate the cell in result workbook, and paste the formula into formula bar. When cell references in new workbook must be different, then I edit the copied formula in formula bar.
After that I can copy the cell with formula in target workbook into range I need it (Of-course with absolute and relative referenced set properly. And in case some formula has different parts with different reference rules, I have to edit the same formula e.g. columnwise too).

The process must be repeated for every different formula I want to copy.

OK. Scrap it!

Simply copy the range in 1st worksheet, activate the left top cell of range where you want the formulas, right-click on selected cell, and from dropdown select 'Paste Special', in Paste special windows check links, and press OK.