The sentence as you use it pertains a little different meaning than the alternatives.
The rows should be copied and pasted to the spreadsheet.
Here the spreadsheet is only the recipient of the copied data. It is perfectly OK to say
The rows should be copied.
The from is only necessary if a source is specified.
The rows should be copied from, then pasted to, the spreadsheet.
The rows should be copied from and pasted to the spreadsheet.
In these cases the spreadsheet is both source and target for the copied rows.
The rows should be copied then pasted to the spreadsheet.
And this gives a time dimension that is not relevant in your original sentence. Of course the copying will usually take place before the pasting (especially when you are talking about the clipboard in todays operating systems), but it might be that the copy-past is done intertwined, reading and writing blocks at the time, which is probably true when copying files. Will say, using then instead of and adds implementation or prozess specific knowledge that might not be necessary in the context.