Assuming that your player characters are Starfleet officers, and assuming that this is a real, permament injury and not something that the aliens make right at the end of the scenario...
You need to ask yourself what life holds for a one armed Starfleet officer.
I think it would be unlikely that one armed officers would continue to serve on starships. Depends on the era of the campaign and the officer's position to a certain extent.
Will he be invalided out of the service? Confined to desk duty? Both of efectively remove the character from the campaign - so you might as well kill him rather than chop off an arm.
Or will he be given a cybernetic arm by Starfleet? In which case watch out for the munchkinism which often seems to follow any such move.
But in general you can run whatever sort of campaign you like and letting your players know early on that it's going to be mean, is better than having them find out later after they've become attached to their characters.
"And all I ask is a tall ship, and a star to steer her by."
"Though a cloaking device, pulsed phaser cannons
and a full load of quantum torpedoes would be quite nice too."