'Pet loss' refers to reactions such as shock and anger that occur in owners who have lost their pet.
Literal
Pet-loss [definitional-とは], pet [object-を] lost owner [to-に] occur shock [and-や] anger [etc.-など] [possessive-の] reactions [object-を] say.
A definition sentence. ~とは introduces the term. ~をいう (is called / refers to) is the standard ending for definitions. ペットロス is a wasei-eigo (Japanese-coined English) term. The relative clause ペットを失った飼い主 defines who experiences it.