The mines might be activated manually.
You're assuming the mines around each tribute's launch pad automatically go off when someone or something touches the ground around them, but this may not be the case. Many of the tricks and traps in the Games are set up and activated manually by the Gamemakers. It could be that they're carefully watching each tribute during the sixty-second countdown and standing ready to explode the mines around any one who steps off their pad.
In this scenario, a tribute who threw their shoe at the ground around the neighbouring tribute, intending to get rid of one of their adversaries before the Games even start, would find themselves blown to bits instead. That would be quite the backfiring plan!
Additionally, I should reiterate one of the points I made in answering your last question
, and which @Richard also made in a comment
on this one:
People who cheat in the Hunger Games usually aren't allowed to win.
Once the tributes are in the arena, they're more or less at the Gamemakers' mercy. It'd be easy for a cheating tribute to be singled out by some mutt or natural disaster, to come to a quick and grisly end. If the Gamemakers really don't want a particular tribute to win, there's no way they'll be able to. It's best to play by the rules unless there's a massive advantage in not doing so.
The only reason Katniss and Peeta were allowed to win after their stunt with the berries was because they were the Capitol's only possibility for a victor. If Cato had still been alive but dying at that point, the Gamemakers would have blown the District 12 'cheaters' sky-high and pronounced Cato the victor. Anyone who cheats isn't someone the Capitol wants walking around forever as a victor - as the fallout from the berries incident, and the third Quarter Quell, demonstrate only too well.
As another example of this attitude from the Capitol, consider what happened to Haymitch after he gamed the system by using the force field around the arena to win his Games:
"No. My mother and younger brother. My girl. They were all dead two weeks after I was crowned victor. Because of that stunt I pulled with the force field," he answers. "Snow had no one to use against me."
"I'm surprised he didn't just kill you," I say.
"Oh, no. I was the example. The person to hold up to the young Finnicks and Johannas and Cashmeres."
-- Catching Fire