"Hebrew mindset" and the "Greek mindset" refers to the fact that there is a difference in their respective way of thinking about life, about God, and about Truth. Both the Hebrews and the Greeks were "set" in their thinking about what and how they believed. To the Hebrew God was an easy concept; He was their Creator.
The Greeks, on the other hand, were more prone to be atheistic or agnostic. That is why Rav Shaul (the Apostle Paul) used different approaches when he spoke to the Hebrew and Greek cultures. In speaking to the Hebrews, he could preach the Gospel directly because they already believed in God and in creation. But in his dealings with the Greeks, he first had to present Messiah Yeshua as the Creator God before actually giving them the Gospel.
Rav Shaul (Paul) points out that the "arm of YHWH" is Y'shua who, while on Earth, is addressed in human terms, where Mari (my Master) is more appropriate. This does not mean that Y'shua is not called YHWH elsewhere but, rather, is a forceful way of identifying the source of this "arm" which relates directly to YHWH's name and His chosen messenger. He is the only "messenger" in the Tanakh with the ability to forgive sin and to officiate in the Name of YHWH, as opposed to the title of "El" (Exodus 23:20-22). The angels all have only YHWH's "title" within their names: Gabri-el, Rapha-el, Micha-el....
Here's something that will blow your mind: The "Greek" mindset imagines a tattoo or something similar on the thigh of Y'shua (Jesus) when he returns as "King of Kings, and Lord of Lords" (Rev. 19:11-13,16). But the Hebrew mindset sees something more realistic: The tzit-tzits (braid/knots/tassels) of Yeshua's tallit (prayer shawl) falling across his thighs when He returns to earth atop a white horse!
What are we saying? Well, each letter of the Hebrew alphabet has a numerical value. Consequently, the knots of the tassels on the four corners of a tallit spell out the name of YHWH....(There are actually different trains of thought about this, depending on how the knots are tied. The Sephardics tie the knots in windings of 10, 5, 6, 5 which spells out the numeric values of "YHWH" but the Ashkenazies use windings of 7, 8, 11, 13 which, adds up to 39, which is the numerical equivalent of Deuteronomy 6:4 which cites the Shema.)
Regardless, the numeric values refer to the only ONE true Name of our ELOHIM - (Yud-Hey-Vav-Hey) - the Name He gave to Moshe (Exodus 3:13-15)! (Please see our article: The Father revealed His Name to Moses.)
Another example of a Hebrew as opposed to Greek mindset can be seen in their respective calendars/timelines. For instance, according to God, a "day" is from "sunset to sunset" (Genesis 1:5) as opposed to "midnight to midnight". He called the days of the week the "first day", "second day", etc., whereas "the world" has named its days and months after pagan gods...