The general principles for distinguishing these two pronunciations are:
When used alone or in spoken language, it is read as "Xie (three tones)"; In written language and compound words, it is pronounced "Xue".
According to this basic principle, the word "blood" in the sentence "How many Chinese sons and daughters wrote patriotic poems with blood and tears" should be read as "Xie (three tones)".
If the word "blood and tears" in this sentence is replaced by "blood and tears", then the word "blood" is read as "Xue".
Appendix:
Among the words "chicken blood", "chicken blood stone", "dog blood" and "dog blood drama", it should be read as "Xie" because these words are all spoken words.