Completely impossible. I don't know where Coro is getting this idea, but Beasley still counts against your cap figure since you amnestied Childress and can't amnesty him too. If Phoenix salary dumps everyone but Dragic and Bledsoe their cap situation looks like:
1. Dragic $7.5M
2. Hold for Bledsoe $6.6M
3. Beasley contract $2.3M
4. Cap hold for empty roster spots under 12 = 10 * $0.47M = $4.7M
So that gives $21.1 million. Subtract that from $63.2 million and you get $42.1 million. Since James and Bosh have more than 10 years in the league, their max is 35% of the cap, or $22.1 million. So you're short $2.1 million even after renouncing everyone but Bledsoe and trading everyone but he and Dragic for nothing.