The two processes suggested so far work from opposite ends of the stream.
Selecting the cell with the formula lets you switch back to the sheet that is to be deleted to check for any table with a highlighted cell, indicating the selected formula is directly dependent on that cell. Not great, because it does not trace the dependency back beyond that direct dependence.

In the example above, the selected cell contains the formula =A2/4, and clicking on that cell reveals that it i dependent on the value in A2 of that table. But it does not reveal that the value in A2 is dependent on the value in A2 of Table 3, that the value in that cell is dependent on the value in B2 of Table 2, and that the value in that cell is dependent on the value of A2 in Table 1.
Selecting the cell you want to test for formulas that depend on it requires testing each suspect cell, but does give an indication of ALL downstream cell depending on that one. Here's the same set of tables with =1/0 (one divided by zero) entered in a cell on Table 1:
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The formula— =1/0 —is guaranteed to produce a division by zero error, as seen in the error note in the image. The rest of the error triangles flag a message that says "Cell “Table 1::B5” contains an error," which could mean that each of the flagged cells makes a direct reference to that cell, or, as in this case, directly depends on a cell who value depends (directly or indirectly) on the value in Table 1::B5.
Better, but unless you have paid attention to structure and pattern in building your tables, you'll need to check the effects of making this test entry on each of the cells in the table you intend to delete, then do a visual search for cells dependent on that value.
A script or Automater service (based on a script) seems a better choice here, even if it eliminate only the need to swap out the current contents of each cell for a formula guaranteed to produce an error, then swap in the previous contents after the user has made a visual check on the cells relying on the contents of that cell, then told the script to check the next cell. Beyond my current field, but likely within SG's, or that of one or more of the other vsitors to this community.
Regards,
Barry