No you cannot connect the SV mkii directly to the computer like say a POD HD500 or BOSS GT-10 that has a direct USB connection.
What you need to connect to a computer in your instance is an audio interface. There are many available in many different price ranges and options.
You would then take the "Studio Out" XLR from the guitar amp and go into the audio interface, then interface to computer. Note that with the SV you are always supposed to have a speaker load connected at all times.
Some mixers also have a USB out on them so they could also be used instead of a regular desktop type audio interface. Hope that helps a bit.
Stormtrooper12's post in Spider Valve MkII 212 - Computer was marked as the answer