In 7.9, i can use the following script to open a new client from my current client. But this script can't work when both our clients upgrade to 8.1. So is there a way to fulfill this function in 8.1?
Java Webstart doesn't exist in current versions of Java. So, no.
There's no direct equivalent, but you should be able to to use system.util.execute to execute another Vision Client Launcher.