The executable invoked by Start-Process is cmd; you must specify its arguments separately, via the -ArgumentList (-Args) parameter, as an array (,-separated):
Start-Process -Verb RunAs cmd -Args /k, calc.exe
Note: The arguments happen not to need quoting here, but --prefixed arguments or arguments with embedded spaces do; quoting is always an option ('/k', 'calc.exe')
Note:
/k is required to keep the cmd console window open after launching calc.exe (/c would close it right after, but in that case you could just skip cmd and pass calc.exe directly to Start-Process).
Generally, you need either /c or /k in order to pass a command to execute to cmd; without that, an argument such as calc.exe is simply ignored.
Run cmd /? for more information.