Can I design Arduino Mega 2560 circuit without adding ATMega 16?
Yes, you can omit the ATmega16U2 and its accompanying parts. That is, the whole right block of schematic in this sheet.

The resulting board will work perfectly fine, it will simply no longer have a built-in programming interface, nor a built-in USB-serial interface. You will likely want to buy an FTDI cable and an AVR programmer, if you do not already have these.