Is my not answering my female cousins’ calls considered a severance of kinship ties, knowing that their calls include details about my life and questions that bother me and force me to lie?

Scholars have differed on the extent of kinship (رحم) whose ties must be maintained. We have favored the view that it is forbidden to sever ties with a forbidden degree of kinship (dhu al-rahim al-mahram) and disliked to sever ties with a non-forbidden degree of kinship (dhu al-rahim ghair al-mahram). Thus, you are not obligated to maintain ties with your paternal cousins' daughters, and there is no blame upon you for not responding to their calls if you fear some embarrassment from them. However, it is not permissible for you to cut them off entirely. Saying Salaam (peace be upon you) is sufficient to end estrangement. It is better for you to respond to their calls, and you can use indirect speech (ma'arid), equivocation (tawriyah), and mollification (mudaraah) without lying.