Praise be to Allah.
If the situation is as you describe, and you try hard to get rid of the blood that accompanies the saliva, by rinsing your mouth and guarding against swallowing any of that, then whatever is left of slight yellow traces in the saliva does not affect you and your fast is valid, in sha Allah.
And Allah is the source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and Companions. End quote.
Standing Committee for Academic Research and Issuing Fatwas
Shaykh ‘Abd al-‘Azeez ibn ‘Abd-Allaah ibn Baaz, Shaykh ‘Abd al-‘Azeez Aal al-Shaykh, Shaykh Saalih al-Fawzaan, Shaykh Bakr Abu Zayd