Can you travel to Venice there and back from Rome in a day?

Yes, you can.

The best option to maximize your time there is to take the night train from Rome to Venice. You leave from the Roma Tiburtina station at 10:50 pm and arrive in Venice at 5:24. You can get a 2nd class seat for 36.50 euro, but it would be better to get a berth in a four bed cuchette for 56.50 euro and sleep through the night. However, check to see if the Amica fare is available - if there are places still available the fare is 45.20 for the cuchette instead of 56.50.

If you don't take the night train, there's a Eurostar at 6:50 from Roma Termini that will get you to Venice at 11:17. There's also an earlier train from Roma Tiburtina at 4:58 am, but you have to change trains in Bologna to arrive at Venice at 10:03.

The latest return to Rome without taking a night train leaves Venice at 6:36 pm and arrives in Rome at 11:08 pm. Note that the train station in Venice is at the opposite end of the Grand Canal from Piazza San Marco. You'll need to allow time to go back and forth, but you would still have a few hours to see Venice.

You could also take the night train back from Venice to Rome. It leaves Venice at 0:04 am (just after midnight) and arrives back in Rome at 6:56 am. Again, you have the advantage of being able to sleep on the train. The return price is the same as above.

Taking the two night trains would give you approximately 18 hours in Venice and use time you'll be sleeping anyway for transit.

Any way you do this will be a very long day - not recommended for everyone, but I make these kinds of trips fairly frequently when there's something I particularly want to see. I've made day trips from Bologna or Verona to Paris, Munich, Nurnberg, Geneva, Pompeii, and Vienna this way over the years.
Yes, you can.

The best option to maximize your time there is to take the night train from Rome to Venice. You leave from the Roma Tiburtina station at 10:50 pm and arrive in Venice at 5:24. You can get a 2nd class seat for 36.50 euro, but it would be better to get a berth in a four bed cuchette for 56.50 euro and sleep through the night. However, check to see if the Amica fare is available - if there are places still available the fare is 45.20 for the cuchette instead of 56.50.

If you don't take the night train, there's a Eurostar at 6:50 from Roma Termini that will get you to Venice at 11:17. There's also an earlier train from Roma Tiburtina at 4:58 am, but you have to change trains in Bologna to arrive at Venice at 10:03.

The latest return to Rome without taking a night train leaves Venice at 6:36 pm and arrives in Rome at 11:08 pm. Note that the train station in Venice is at the opposite end of the Grand Canal from Piazza San Marco. You'll need to allow time to go back and forth, but you would still have a few hours to see Venice.

You could also take the night train back from Venice to Rome. It leaves Venice at 0:04 am (just after midnight) and arrives back in Rome at 6:56 am. Again, you have the advantage of being able to sleep on the train. The return price is the same as above.

Taking the two night trains would give you approximately 18 hours in Venice and use time you'll be sleeping anyway for transit.

Any way you do this will be a very long day - not recommended for everyone, but I make these kinds of trips fairly frequently when there's something I particularly want to see. I've made day trips from Bologna or Verona to Paris, Munich, Nurnberg, Geneva, Pompeii, and Vienna this way over the years.