A newly displayed header isn’t necessarily new. It may be a repeated header. In this case you can delete a column stretching over more than one pages as Pedro described.
If you have actually many tables of the same structure and headers that might simply be bad design. If there is no text between the tables (or only text that can be deleted - empty paragraphs included) you may merge the equally structured tables: If there are mergeable tables and the cursor is positioned in the first row of the second one there will be an item ‘Merge Tables’ in the same context menu we talked already about.
All the other cases: You will surely much faster delete the first columns from some dozen tables than I (or someone else) can write a macro for the task and explain to you how to apply itk.