Uno as ISP for Atmega 1281

What pins are you connecting to? On the 1281/2561 the programming pins are not SCK/MOSI/MISO, they are elsewhere.
In repsonse #20 here you can see where I jumpered from an FTDI header to the ICSP header to connect two of the signals.
https://forum.arduino.cc/index.php?topic=380757.15