People of mixed Jewish/Non-Jewish blood were called "Mischling". tl;dr, you would likely be considered a second degree Mischling.

The Nazis had a two tiered test to determine someone's "Jewishness".

Part One:

If you have 3 or 4 Jewish grandparents, you are a Jew.

If you have 2 Jewish grandparents, you're either a Jew or a first degree Mischling pending the second part of the test.

If you have 1 Jewish grandparent, you're a second degree Mischling.

Part Two:

If you have two Jewish grandparents, you're asked a series of questions that determine if you're a first degree Mischling or full blown Jew.

If you were a member of a Jewish community on or after 14 November 1935, you're a Jew.

If you marry/are married to a Jew on or after 14 November 1935, you are also a Jew.

If your parents were married on or after 17 September 1935 and one of them was Jewish, you are also a Jew.

If you're born out of wedlock on or after 31 July 1936 with one Jewish parent, you're a Jew.

With regards to you, this all depends on whether your grandfather was considered a Jew or first degree Mischling under Part 2 of the test.

You said your grandfather had a Jewish mother and non-Jewish father. In Jewish communities, the idea of "being Jewish" is passed down through the mother. So most Jewish communities would've accepted him as Jewish. The thing is, were his mother's parents (Your great great grandparents) BOTH Jewish (Hence making your grandfather's mother fully Jewish) ? You need to apply the test going back all those generations until you can ascertain who was definitely and definitely not a Jew under Nazi law. I can't say for certain with the information you've provided. And likely you'd need to do some digging around family records and asking relatives to find out yourself.

But if we assume your great grandmother had two Jewish parents, and was inarguably a Jew herself, then your grandfather would go to part 2 of the test, as he had 2 Jewish grandparents.

So if my assumption, that your great grandmother was fully, or otherwise considered to be, a Jew, just apply Part 2 of the test to see if he was a first degree Mischling or a Jew.

Now, if your grandfather is considered a Jew under Part 2 of the test, then according to Part 1, you are a second degree Mischling. That I'm aware of, there was no formal policy in place to discriminate those descended from Mischlings. So if your grandfather is a first degree Mischling under Part 2, you would not be considered Jewish.

There was a handy chart disseminated for the relatively complicated job of determining who, for the purposes of the Nuremberg laws, was Jewish, who was German, and who was a Mischling (in between, basically). This thread has a translated version. The really complicated part comes with who can marry who, which is a decent portion of the chart. If I'm reading the chart correctly, your grandfather, with half Jewish ancestry, would be a first-degree Mischling. Your father, with one parent with half Jewish ancestry, would be a 2nd degree Mischling. You, with one second-degree Mischling parent, would simply have been considered German.

Despite the Nazi's love of charts and formalized procedures, reality was much more complicated. The Mischling as a legal category only really existed in Germany. In the East you simply were either Jewish (in which case, you would be killed or enslaved, or put in a ghetto and one of the previous things would happen to you eventually). This was aided by Eastern Europe having far less historical intermarriage between Jews and non-Jews than Western Europe had.

In Western Europe treatment of mixed people varied quite a bit. They were subject to discrimination, but they generally were not all treated as though they were Jews. There are probably others around here who can answer the details of that better than I can. But in the end, a person with one Jewish great-grandparent probably would not have been subject to a whole lot of mistreatment because of it.