Travel to Vis Island is straightforward: you take a ferry to Vis Town from Split. Jadrolinija runs the year-round car ferry to Vis and Krilo runs the year-round catamaran. It's a long ride, though--about 2 1/2 hours. See the Split-Vis car ferry schedule.
Most of the year the ferry schedule makes it impossible to visit Vis Island as part of a day trip from Split as the ferries leave Vis Island in the morning and leave Split in the afternoon. Some morning catamarans from Vis make a stop in Hvar Town before going on to Split in time for islanders to get to their jobs. See the Split-Hvar-Vis catamaran schedule.
From June to September however you can visit Vis Island as a day trip from Split (but not Hvar) as there is a car ferry that leaves Split in the morning and returns in the afternoon. In Vis Town, a bus to Komiza meets the car ferry and returns in the afternoon to catch the afternoon ferry. It's enough time to take a look around Vis Town and Komiza but not enough time to visit the Blue Grotto of Bisevo. For that you need to stay the night.
Taking a car aboard your ferry to Vis Island doesn't make sense for a day trip. It's expensive! You'll do much better renting a car for a day from a rental agency in Vis Town.