Yes, you can make him shoot again but you have a couple of options.
1- You can replace the ball and have the opponent replay it from the original location but you're now entering the murky world of the MISS RULE (see below)
2- You can make them shoot again from where the cue ball finishes. If the cue ball finishes in a open location with easy shots available obviously you won't put him back or have them play from there.
I would recommend you avoid trying to implement the miss rule when playing recreationally or at the amateur level.
The ability to escape a snooker varies greatly from amateur to pro and the miss rule was created with pro skill set in mind.
The reason the miss rule was implemented is because some of the more cagey pros would intentionally avoid trying to make the easiest escape/hitting the ball on because the shot was guaranteed to leave the opponent in.
The basic premise is that if you have a ball you can hit either directly or off one rail, at the pro level you must hit it. If you elect to take on a two or more rail escape instead of the easily hit ball in order not to leave a shot on that would be deemed a miss if you don't hit it. It's assumed at the pro level you will always hit the ball on if you have a direct or one rail shot available so it's deemed a "miss" if you don't hit any.
Final recommendation to the rec players.....have your opponent either play from where it finishes or if the position is nice, enjoy the spoils of your snooker. Don't bother putting them back unless it's incredibly obvious they made no attempt at all to escape the snooker