You are aware that copper is tubing and tubing is specified by inside diameter. Fittings like shut off valves are commonly specified by the tube inside diameter on their plastic bags or blister packs as well even though the item interfaces with the outside diameter when being installed.
Confirm you are referring to the inside diameter re "1/2" copper pipe stubout".

The most important rule in DIY... always start DIY projects at 8AM. The time most parts stores open.

The second most important rule in DIY comes from Clint Eastwood in Magnum Force... "A man's got to know his limitations"

Take the piece you cut off to the store and get the correct angle stop for that size tubing.

1/2" copper pipe is 5/8" OD,,therefore the fitting he has is the correct size for the pipe he is working on...

Having said that, it then comes down to this..those push on type fittings ARE NOT code approved for potable water service..

The simple solution is to get a 1/2"ID (5/8"OD" x 3/8" output COMPRESSION TYPE angle stop. You the clean the end of the line, slip the compression nut on the line, then slip the compression ferrule on the line, slide the valve on until it stops, then slide the nut forward to meet the valve and tighten the nut finger tight, then hold the valve with one wrench while tightening the nut with a second wrench and you will have an ASTM approved connection and you can sleep good without worrying about will that DIY junk hold up.

The Pup is right again and the OP has the answer as long as he cut the tubing with a tubing cutter and not a sawzall ;-)

".....cut the tubing with a tubing cutter and not a sawzall...."

Regret to admit I know exactly what you mean. Experience can be a harsh teacher.