Can I used a 10 Amp relay on 220v power supply of computer?
Maybe I can save electricity by using relay to totally unplug the computer.
Why? A modern computer is already designed to conserve energy. If you insist on reinventing the wheel, just use a double pole switch, a relay needs a power supply and some means of turning the relays on and off.
Why not? Each PC uses 1 ... 5W in standby, makes ~ 40 bucks a year. If you have switches/routers on the same powerline, they consumer ~ 3-10W. If you have more than one PC, ... well, you can do the maths. And a double pole switch is definitly the way to go. There are master-slave-socketboards out there, they usally use a solid state relais.
Each PC uses 1 ... 5W in standby, makes ~ 40 bucks a year.
Absolute Rubbish. Who pays $1 per kilowatt hour for electricity?
There are other countries besides USA 
Yes you can do it , but .....
You have to factor in the extra power used by any circuit used to switch the PC on and off and what it will do if it accidentally chops the pc power rather than correctly shutting it down . Add the cost of your new switching device .
You also need to factor in the fact that when the computer is in use , you can’t count the cost of its standby power in your sums for standby consumption .
I expect the cost effectiveness has fallen a fair bit now.
Just pull the plug out , look at better energy saving schemes - light bulbs, insulation ,fixing draughts etc .
Using the illustrated module would be a bit dubious. If you choose to switch both poles of the supply you must do it with a double pole switch, otherwise there is a risk that if it does not quite work, it interrupts only the neutral - not a good idea.
Picked up one of those Jackson "Prevent Power Wastage" power boards at a garage sale a couple of weeks ago (I think) - not sure whether it was a dollar or two objects for a dollar. Since this is mentioned, I just got out the snake eyes and took a look at it. Its power supply is capacitive but has a 3 W resistor before the Zeners, a 24 V "Songle" relay not unlike the picture at top and uses a current transformer in the neutral line ("minimum load 35W") and a LM324.
I wasn't sure whether to get it at the time as I cannot really think of a use for it but hey! It was just so cheap. 
(Got some nice LED Christmas lights today, two strings for $3 each and a rechargeable 30-odd LED work light for $2.)