I wouldn't day trip from Seville to Granada. The 2-1/2 hours (at least) on the train each way is just part of the travel time. First you must get to the train station in Seville, which probably won't be terribly close to where you're staying. Then, when you arrive in Granada, you're nowhere near the Alhambra and must take either a tram or a taxi over there. At the end of your sightseeing day you'll need to do those things again, in reverse.
Seeing the Alhambra can be nearly a full-day activity. Yes, you can rush a bit, but it's still going to take a lot of time, and what about lunch? I don't see that you'd have time to do anything other than the Alhambra.
Are you early risers? If you don't catch the 7:42 train or the 8:01 train, the next departure's at 9:43 AM, and it doesn't get you to Granada until 12:24 PM.
The last two relatively fast (less than 3 hours' travel time) trains back from Granada leave at 6:57 and 7:25 PM. You certainly wouldn't want to return on the 3:35 PM train. Even the 7:25 PM train would give you less than 6 hours of sightseeing time.
There are also ALSA buses connecting Seville and Granada. They take a more direct route than the trains, but they're scheduled to take 3 hours and could potentially suffer from traffic delays.