Purity: Performing Wudu Or Ghusl Conflicts With Another Legal Responsibility That Is More Important Or Just As Important

Practical Laws of Islam as per the teachings of Ayatullah Sistani

Ruling 665:

If someone has a little water and his body or clothing is impure, and were he to perform wuḍūʾ or ghusl with that water there would not be enough left over with which he could wash his body or clothing, he must wash his body or clothing with the water and perform prayers with tayammum. However, if one does not have anything with which he can perform tayammum, he must use the water for wuḍūʾ or ghusl and perform prayers with his impure body or clothing.

Ruling 666:

If a person only has water or a utensil [in which there is water] that is unlawful to use – for example, the water or utensil is usurped and he does not have any other water or utensil – he must perform tayammum in place of wuḍūʾ and ghusl.

-Ayatullah Sistani, Practical Laws of Islam, Purification (Taharah)