Actually what you wrote should work.
I use this:
$JMP_path = "C:\Program Files\SAS\JMP\15\Jmp.exe"
$JMPScriptPath = 'C:\MyScript.jsl'
Start-Process -FilePath $JMP_path -ArgumentList ("`""+$JMPScriptPath+"`"") -Wait
What I would like to add to this is to pass another variable into the script. Any idea how to do that?