Checkbox in Table 1 add or remove data to Table 2?

Sounds like you want to create a link to the other table and use lookup fields to pull that data into the other table.

But would the link and data go away if I uncheck the box in the originating table?

No.  So essentially, you want a processing queue?  Data comes into table 1, search for the item in table 2.  If found updated record, if not found create record.  When complete delete data from table 1? 

I would do this with 2 automations.  1 does everything but the delete.  In the update/create step set a flag in Table 1 that marks is as "processed".  Then your second automation that says when a record in table 1 is "processed" run a script to delete the record.  You can only delete records in a script.

If I'm understanding correctly, you started off the automation with the correct trigger, but you'll need to use conditional actions if you want everything in one automation. You'd set the condition to if the box is checked and then add an create a record action with what you want it to put in the other table. And another set of conditional actions for if the box is unchecked, with a find records action and run a script action to delete the record.