Dexter always uses this boat to get rid of his kills but in Season 2 he gets into trouble for it, first by wiping his boat clean in front of recently installed security cameras, which he has to hastily remove the file of (Dex, Lies and Videotape) and a second, much worse time where James Doakes attaches a GPS Tracking Device onto his boat and follows him to a kill site where he confronts him and discovers Dexter's secret (Resistance is Futile).
He also tends to use the boat as a means to bond with people, such as getting back on Rita's good terms by taking her and the kids on a fishing trip at the end of season 2 (Left Turn Ahead). He also goes fishing with Miguel Prado in the middle of season 3 and takes Debra, Rita and the kids on a trip in the middle of season 4.
In Season 7, Louis Greene attempted to sink the Slice of Life, Isaak Sirko comes across Louis and shoots him in the head and he dies on Dexter's boat. George takes him out to sea and dumps his body somewhere in the ocean. Later in the season it seems that Louis' attempt to sink the Slice of Slice was unsuccessful as Dexter was seen with it in the ocean furthermore Dexter discovered Louis' death and proceeded to clean the boat.
The name itself is a pun on Dexter's secret life as a serial killer, "slice" referring to his use of blades.