Slog/sweat/work/flog your guts out British informal hyperbole
To work very hard for something
The researchers have slogged their guts out for months on this research.
Justin has been working his guts out getting a scholarship to Germany.
My mom sweated her guts out all her life for us.
An industrious person
Very busy
To work extremely hard
Show signs of great and arduous efforts or labour on study or tasks leading to the result of tiredness and lack of vitality.
Someone is extremely boring, often due to being very studious or introverted.
The verbs work/slog/sweat are conjugated according to the tense of the sentence.
Despite of its unknown source, the phrase is used as a hyperbole to stress the amount of effort you put in order to achieve a certain goal. Slog and sweat are two verbs which stress the hard-working attitude, so to slog/sweat/work your guts out can mean that you are willingly work until you exhaust yourself to achieve the goal you desire