Is there a formula to copy and paste cell values from one sheet to another?

> I know I can select cell D1 from sheet 2 and use formula "=A1" to reference cell A1 from sheet 1 into cell D1 on sheet 2, but I need it to actually paste the value from A1 into D1, so if I deleted sheet 1, the values would still show on sheet 2.

That's what Edit -> Copy Snapshot does

It copies just the values of the selected cells. When you paste, you get those values, disconnected from the original cells they were copied from.

Then no, at least not directly.

A cell can either contain a formula (including a reference to another cell) or it can contain a static value (text, number, date, etc.). Any cell can pull data from another cell, but there's no direct way to push data into another cell.

The only way I can think of to do what you describe is via some external script that copies the table (or its values) between the sheets. There are a few ways of doing that, depending on the end goal (e.g. do you want a direct copy of the table, or just specific cells?)