Using Automator to save text to a SPECIFIED text file (not a new file)
You could use an Automator workflow/application using a Run Shell Script action with:
/usr/bin/pbpaste &gt;&gt; '/path/to/filename.txt'
echo &gt;&gt; '/path/to/filename.txt'


Notes:
Check out the manual page for: pbpaste
You can read the manual page for command in Terminal by typing command and then right-click on it and select: Open man Page
The echo &gt;&gt; '/path/to/filename' line adds a single line feed to the end of the file after the pasted text. You can add addition lines for more line feeds if you so choose.
In place of the echo command you can also use, e.g.:
printf '\n' &gt;&gt; '/path/to/filename.txt'

Adding additional \n for more line feeds, e.g. '\n\n'.
If you update the file while it's opened, it is not doing to show the updated contents, you need to close/reopen the file to see additional updates to it.




If you want to do it with AppleScript, then in place of the Run Shell Script action, use a Run AppleScript action with the following example AppleScript code wish uses a slightly modified handler from Reading and Writing Files:
set myFilename to (path to documents folder) &amp; &quot;Clipboard Text.txt&quot;

set cbText to ((the clipboard) as text) &amp; linefeed &amp; linefeed

writeTextToFile(cbText, myFilename, false)


on writeTextToFile(theText, theFile, overwriteExistingContent)
    try
        -- Convert the file to a string
        set theFile to theFile as string
        -- Open the file for writing
        if theFile contains &quot;/&quot; then
            set theOpenedFile to open for access theFile with write permission
        else
            set theOpenedFile to open for access file theFile with write permission
        end if
        -- Clear the file if content should be overwritten
        if overwriteExistingContent is true then set eof of theOpenedFile to 0
        -- Write the new content to the file
        write theText to theOpenedFile starting at eof
        -- Close the file
        close access theOpenedFile
        -- Return a boolean indicating that writing was successful
        return true
        -- Handle a write error
    on error
        -- Close the file
        try
            close access file theFile
        end try
        -- Return a boolean indicating that writing failed
        return false
    end try
end writeTextToFile


Notes:
The handler from the linked Apple support document was modified to handle both POSIX and HFS+ file paths.