Both boys were born to Mina prior to 1900 and it's possible that Mina didn't tell "the truth and the whole truth" to Reuben Joshua Grubaugh. In 1910, Mina does admit to being married earlier (M2), but still lists neither of her earlier two boys.
In 1900, both boys are listed with Mina's parents, Jesse and Margaret Wynn, in Knox County, OH. John is listed as John Newton, born Oct 1893 in Missouri, and Walter Wise is listed as such, born Feb 1897. I believe Margaret died sometime shortly after 1900 and Walter can be found in an orphan's home in 1910.
John eventually changes his surname to Wynn and can be found in the World War I draft registration in Buckeye, Ashland, OH. He lists his birth location as being Mountain Grove, Wright, MO. I have no idea why Mina would have gone to Missouri to have a child, but, since John later changes her surname to Wynn, his conception may have been outside of wedlock.
Walter is also found in the World War I draft registration in Richland County, OH and you can see he doesn't know much about his birth. Walter and his wife, Thelma, are buried in Ashland Cemetery and can be found in Find-a-Grave.
John Wynn married Minnie Mae Rowland in November 1912 in Ashland County. His marriage record can be found in the new LDS pilot site database, Ohio Marriages, 1800-1958. He lists his mother as Mina Wynn. He married Mabel Agnes Kelly on 18 Oct 1916 (also in Ashland County) and he is still living at the time of her death in 1951.
Since Mina admits to having been married at least once before, it was likely to a ?? Wise, who fathered Walter.
Hope this helps