You can cut bread without "slicing" it - you can cut it in half, you can cut the crusts off.
In my own case, I would differentiate between "cutting a slice of bread" and "slicing a whole loaf of bread" - when I use "slice" in a sentence like this, I'm talking about cutting it into multiple slices, and the NEID suggests gearr ina shlisní ("cut into slices") or slisní a dhéanamh de ("to make slices of") for that sense of slice.
In short, you could translate "I slice the bread" into Gearraim an t-arán, but you shouldn't really translate Gearraim an t-arán into "I slice the bread".
That is purely a personal opinion as the definition of cut is to divide into pieces with a knife or other sharp implement.
"cut the beef into thin slices"
synonyms: chop, slice, dice, cube, mince, carve, hash
"cut the pepper into small pieces"
That being said however there is no guarantee that duo lingo agrees they mean the same thing
In the nominative/accusative case, masculine nouns that start with a vowel get a t- prefix after the singular definite article an.
Tá an t-arán ar an bpláta (nominative)
Itheann sé an t-arán (accusative)
In the dative and genitive, you don't get a t- prefix. For the most part, you will use the dative when the noun is the indirect object after a simple preposition (ag, ar, etc).
tá im ar an arán (dative)
tá sé ag ithe an aráin (genitive)