I'm not sure what the monks recite when they go to the fields, but there is a mantra that one can recite to ensure we do not collect negative karma when we accidentally step on small creatures like ants etc. It is called "Blessing the feet": "Om Kretsara Ghana Hum Hri Soha". We recite the mantra 3 times and spit on the soles of the feet.
Whether we eat part of a cow or five sardines, it is still negative karma. So it is better to refrain from eating meat. If we believe that all sentient beings had been our mothers or our relatives etc in previous lives, then it is like eating our relatives. If we believe in karma, this means that in a future life we will suffer the consequences.
In "Food of Bodhisattvas", Shabkar Tsogdruk Rangdrol says if we eat the flesh and blood of beings who were once our mother or our fathers, we will, in a future life, take birth in the hell of Screaming, which, of the eighteen, is one of the hot hells... And even when we are born again in this world, for 500 lives we will take birth in monstrous and devouring forms. We will become demons, ogres, and executioners. It is said too that we will be born countless times among the outcasts, as butchers, fishermen, and dyers, or as carnivorous beats thirsting for blood: lions, tigers, leopards, bears, venomous snakes, wolves, foxes, cats, eagles, and hawks."
Thus, it is clear that meat-eating is a major obstacle for the gaining of a high rebirth as a human or a god.