There are some awesome hidden derashot on Zevachim 107a. (I call a derash hidden if there is a surface and superficial way of reading it that seems 'light', but an alternative way of reading it with greater depth.)
הדתנן הזורק מקצת דמים בחוץ חייב מנלן
נפקא ליה מדתניא
דם יחשב לרבות הזורק דברי רבי ישמעאל רבי עקיבא אומר או זבח לרבות את הזורק
The 'straightforward' understanding of Rabbi Yishmael's derasha requires that we consult Rashi, who includes a later phrase from the pasuk as well (matching how they brayta appears in Sanhedrin):
דם יחשב דם שפך - לרבות את הזורק והאי קראי בשחוטי חוץ כתיבי:
That is, it is considered 'blood' guilt (liability) for spilling (throwing) blood. That is how Artscroll (footnote 16, in brackets) explains the difficult derasha.
I would suggest that the derasha simply focused on the words 'dam yechashev'. The peshat is that for **slaughtering** the sacrifice outside the Temple, it is considered bad, bloodshed, blood-guilt, shedding of blood. Rabbi Yishmael, in order to arrive at a (previously known?) halacha that throwing the blood also counts, narrowly focuses on the words 'dam yechashev' out of context (significance maximalism, context minimalism) and translates it as 'blood is also reckoned'.
What about Rabbi Akiva? His derasha is:
או זבח לרבות את הזורק
The full pasuk for Rabbi Akiva is:
וַאֲלֵהֶ֣ם תֹּאמַ֔ר אִ֥ישׁ אִישׁ֙ מִבֵּ֣ית יִשְׂרָאֵ֔ל וּמִן־הַגֵּ֖ר אֲשֶׁר־יָג֣וּר בְּתוֹכָ֑ם אֲשֶׁר־יַעֲלֶ֥ה עֹלָ֖ה אוֹ־זָֽבַח׃
The simple meaning is that the pasuk is talking about someone who offers a burnt offering (olah) or a sacrifice (zevach), but outside the Temple. And the simple derasha is that since it does not say 'olah u-zevach', using the 'and' conjunction, but instead adds a whole word (and an alef) to make it 'olah `o zavach', using the 'or' conjunction, this is a 'ribbuy', an inclusion. And we can use inclusions to include whatever we like which is somewhat related to the context, so we are including not just the act of bringing the korban, but also the act of sprinkling. (And so the gemara goes on the 'or' being used to divide, that one need not bring both an olah and a zevach, and then goes on a sytematic derasha chain, how each interprets the others source text.)
I would suggest an alternative understanding of the derasha. The last word in the pasuk is zevach. But since it is the last word of the pasuk, it takes on a pausal form, zavach, with a kametz, yet retaining the stress on the first syllable. With the 'and' connective, it would be clear that this is a noun, and the 'olah uzavach' are the object of 'asher yaaleh'. With the 'or' connective, the word zavach can be read as a verb instead. Namely, the past tense of 'zoveach'. Then, there are two actions. Asher = who. Yaaleh olah = brings (ascends) a burnt offering. O Zavach = or who was 'zoveach'. And this other action would then be the closely related act of 'yaaleh', namely sprinkling the blood.
הדתנן הזורק מקצת דמים בחוץ חייב מנלן
נפקא ליה מדתניא
דם יחשב לרבות הזורק דברי רבי ישמעאל רבי עקיבא אומר או זבח לרבות את הזורק
The 'straightforward' understanding of Rabbi Yishmael's derasha requires that we consult Rashi, who includes a later phrase from the pasuk as well (matching how they brayta appears in Sanhedrin):
דם יחשב דם שפך - לרבות את הזורק והאי קראי בשחוטי חוץ כתיבי:
That is, it is considered 'blood' guilt (liability) for spilling (throwing) blood. That is how Artscroll (footnote 16, in brackets) explains the difficult derasha.
I would suggest that the derasha simply focused on the words 'dam yechashev'. The peshat is that for **slaughtering** the sacrifice outside the Temple, it is considered bad, bloodshed, blood-guilt, shedding of blood. Rabbi Yishmael, in order to arrive at a (previously known?) halacha that throwing the blood also counts, narrowly focuses on the words 'dam yechashev' out of context (significance maximalism, context minimalism) and translates it as 'blood is also reckoned'.
What about Rabbi Akiva? His derasha is:
או זבח לרבות את הזורק
The full pasuk for Rabbi Akiva is:
וַאֲלֵהֶ֣ם תֹּאמַ֔ר אִ֥ישׁ אִישׁ֙ מִבֵּ֣ית יִשְׂרָאֵ֔ל וּמִן־הַגֵּ֖ר אֲשֶׁר־יָג֣וּר בְּתוֹכָ֑ם אֲשֶׁר־יַעֲלֶ֥ה עֹלָ֖ה אוֹ־זָֽבַח׃
The simple meaning is that the pasuk is talking about someone who offers a burnt offering (olah) or a sacrifice (zevach), but outside the Temple. And the simple derasha is that since it does not say 'olah u-zevach', using the 'and' conjunction, but instead adds a whole word (and an alef) to make it 'olah `o zavach', using the 'or' conjunction, this is a 'ribbuy', an inclusion. And we can use inclusions to include whatever we like which is somewhat related to the context, so we are including not just the act of bringing the korban, but also the act of sprinkling. (And so the gemara goes on the 'or' being used to divide, that one need not bring both an olah and a zevach, and then goes on a sytematic derasha chain, how each interprets the others source text.)
I would suggest an alternative understanding of the derasha. The last word in the pasuk is zevach. But since it is the last word of the pasuk, it takes on a pausal form, zavach, with a kametz, yet retaining the stress on the first syllable. With the 'and' connective, it would be clear that this is a noun, and the 'olah uzavach' are the object of 'asher yaaleh'. With the 'or' connective, the word zavach can be read as a verb instead. Namely, the past tense of 'zoveach'. Then, there are two actions. Asher = who. Yaaleh olah = brings (ascends) a burnt offering. O Zavach = or who was 'zoveach'. And this other action would then be the closely related act of 'yaaleh', namely sprinkling the blood.
