I am using the remove command as so:
Remove(Table1, 'Main Data Table'.Selected)
However this doesn't actually change the table, only the display on powerapps' side. Is there a way to have this command change the table itself in the same way many of the other powerapps commands do?
If your data source is a table named Table1 in an Excel file residing in either DropBox or OneDrive and you have selected a record in either a datatable control or a gallery control, Remove (Table1, Gallery1.Selected) or Remove(Table1, DataTable1.Selected) should remove it from the Excel table. However, you may want to check to see if the data source for your Remove function is a collection derived from an excel data source and not the data source itself. If it is, that would explain why the record is removed from the display and not from the underlying Excel table.
Unfortunately that isn't the case which is why I am confused as to why it isn't working. The formula is connected directly to the DataTable from excel and yet still isn't changing the table. My other commands linked to the same table (submit, edit etc) are working and changing that table.
Can you clarify a few things more explicitly:
Are you having the exact same issue as @Anonymous?: