The real beginning of the end was the Denny Neagle trade. Neagle by himself was good, no question and he was likely worth what he was paid. However, the Braves traded Corey Pointer (Braves 2nd round pick in the 1994 draft, think Demeritte), Ron Wright (7th round 1994 pick who was one of the top 100 players in miLB - think Riley) and Jason Schmidt (8th round pick in 1991 draft, one of the top pitching prospects in all of baseball - think Soroka, 31.8 career WAR with highs of 6.7 and 6.8 and 2 top 5 CY finishes) for Neagle. Then they had to resign Neagle which they did which directly or indirectly led to the need to trade David Justice and Marquis Grissom for payroll reasons for Alan Embree and a pending FA in Kenny Lofton, which also required the trade of Jermaine Dye (20.3 War, 1 top 5 MVP) and Jaime Walker for Keith Lockhart and Michael Tucker. Both Schmidt and Dye had about 5 years of team control when traded. March 1997 was a horrible month for the Braves.
After the damage was done and Neagle had worn out his welcome in Atlanta, Tucker, Neagle and Rob Bell were traded to Cincy for Brett Boone and Mike Remlinger.
So, in effort to get Neagle for the stretch run in 1996, a year when they had Maddux, Glavine, Smoltz and Avery that they were paying (plus spot starters Bielecki and Wade), plus Schmidt (who outpitched Neagle in 1996 after the trade), JS set into motion a number of moves that would cause trouble for years. It's not that Neagle was a bad pitcher. He wasn't. In fact he was very good in 1997 (still no better than the 4th best pitcher on the club) and 1998 (again 4th best) before being traded.
But he was a luxury at a position where they couldn't afford it and they traded away value that haunted them for years. Can you imagine a rotation with Maddux, Glavine, Smoltz, Millwood and Schmidt and an OF of CF AJ, LF Grissom, RF Justice/Dye?
It was a bad trade that on the surface doesn't look like a bad trade.