He works as a cleaner in a butcher shop and he is asking about the blood that gets on his clothes whilst he is working

With regard to “blood poured forth” that comes out of the animal at the time of slaughter, it is najis (impure) according to scholarly consensus. 

With regard to the blood that is mixed with the meat or that remains in the veins, it is not called “blood poured forth” and it is taahir (pure). 

Imam at-Tabari (may Allah have mercy on him) said: 

In the verse in which Allah tells His slaves that blood is haraam, He mentions “blood poured forth” (al-An‘aam 6:145), to the exclusion of other types of blood. This clearly indicates that blood that is not “poured forth” is halaal and not najis. 

Then he narrated from ‘Ikrimah the words: Were it not for this verse, the Muslims would have had to trace out the blood from the veins as the Jews do. 

It was narrated from Abu Majlaz, concerning the reddish colour that may appear in the cooking pot because of blood, that he said: Allah has only forbidden “blood poured forth.” 

It was narrated from ‘Aa’ishah that she did not see anything wrong with the reddish colour or blood that may appear in the cooking pot, and she recited this verse (interpretation of the meaning): “Say (O Muhammad SAW): I find not in that which has been inspired to me anything forbidden to be eaten by one who wishes to eat it, unless it be Maytatah (a dead animal) or blood poured forth (by slaughtering or the like)…” [al-An ‘am 6:145]. 

Tafseer at-Tabari, 12/193-194, Shaakir edn. See also: Tafseer Ibn Katheer, 6/194-195. 

Al-Mirdaawi (may Allah have mercy on him) said: 

The blood of animals that may be eaten is taahir, according to the correct view of the madhhab, even if its reddish colour appears. This was stated and it is the correct view of the madhhab… Because the veins are part of the meat and cannot be separated from it, so the ruling (on blood) is waived, because it cannot be helped. 

Al-Qaadi said: As for the blood that remains in the meat after slaughter and what is left in the veins, it is permissible. Shaykh Taqiy ad-Deen said concerning it: I do not know of any difference of opinion about overlooking it and that it does not make the broth najis; rather it may be eaten with it.

End quote from al-Insaaf by al-Mirdaawi, 1/309 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Blood that remains in the slaughtered animal after it is slaughtered, such as the blood in the veins, heart, spleen and liver, is taahir whether it is a little or a lot.

End quote from ash-Sharh al-Mumti‘, 1/440 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked: 

Is prayer acceptable in clothes that are spattered with the blood of the sacrificial animal? If a person prayed with blood on his clothes, what should he do? Where is the problem; is it the blood that is spilled whilst slaughtering or the blood that is left in the meat? 

He replied: The clothes must be washed or changed; he cannot pray in them when they are contaminated with blood. He must either wash them or change them; he should wash them and delay the prayer until he has washed them. If he knew about the blood and when ahead and prayed deliberately, then he has to repeat his prayer. If he forgot or was unaware of it, he does not have to repeat his prayer. If he did it deliberately and knowingly, and was heedless, then he has to repeat his prayer. What is referred to is the “blood poured forth” that comes out at the time of slaughter. As for the blood of the meat itself, it does not matter. The blood that remains in the muscles and veins is overlooked. What is meant here is the blood that comes out at the time of slaughter.

End quote from Majmoo‘ al-Fataawa, 29/219 

To sum up: 

If the blood comes from the carcasses of animals that were slaughtered a few days ago, as you say in your question, there is nothing wrong with it; rather it is taahir. 

If it came from an animal at the time of slaughter when it was still alive, then this is najis blood, but if it is only a small amount, then it is overlooked, especially for someone like a butcher for whom it is difficult to avoid that. 

And Allah knows best.