Leviticus 7:27 reads:
כָּל נֶפֶשׁ אֲשֶׁר תֹּאכַל כָּל דָּם וְנִכְרְתָה הַנֶּפֶשׁ הַהִוא מֵעַמֶּיהָ
"Every soul which would eat all (types) of blood will be cut off from its people."
I have translated וְנִכְרְתָה as being definitively in the future, as it is an instance of a phenomenon referred to by scholars as the "Waw Consecutive." The Waw consecutive occurs in narrative verses in the Torah, and is characterized by a verb prefixed with the letter Waw (ו) changing its tense from perfect to imperfect (as in the verse above), or vice-versa from imperfect to perfect.
Several scholars attribute the Waw Consecutive as a being a feature of East Semitic languages (Hebrew is a West Semitic language), and there is an excellent Wikipedia article which discusses this. Consider the following verse from Deuteronomy 34:6:
...וַיִּקְבֹּר אֹתוֹ בַגַּי בְּאֶרֶץ מוֹאָב
"And He buried him (Moses) in the valley, in the land of Moab..."
The scholar Robert Hetzron explains the word וַיִּקְבֹּר as follows:
וַיִּקְבֹּר (accent on last syllable) < וַהַוׇה יׅקְבֹּר (accent on first syllable of יׅקְבֹּר)
"He buried" < "And so it was that He buried"
In Biblical Hebrew, and hypothetically in Akkadian, an East Semitic language, the form יׅקְבֹּר (yiqbór), with its accent on the last syllable, means "He will bury." However, in Akkadian יׅקְבֹּר (yíqbor), with an accent on the first syllable, would have meant "He buried" in the past. This form of the verb (yíqbor) no longer exists in Hebrew outside the Waw Consecutive construct. Because of the confusion between the past and future forms which looks so similar, it became common practice to insert וַהַוׇה "and so it was" in front of this obsolete past form, leaving us with וַהַוׇה יׅקְבֹּר for "He buried." Over time, וַהַוׇה was shortened to just the letter Waw (וַ). Hetzron explains the Waw Consecutive with the Biblical Hebrew past tense as an analogy to what has just been explained here about the imperfect.
Your second question centered around whether being cut off could be the cause of the sin, which in the case of Leviticus 7:27 is eating blood. I believe this assumption depends in part on וְנִכְרְתָה being interpreted to mean "and [that soul] has been cut off." If וְנִכְרְתָה could have a past meaning, the verse might seem to be implying that the soul had already been cut off before the person ate the blood. However, since we must translate וְנִכְרְתָה in the future, it seems clear that the act of eating blood is causing the soul to be cut off.