Why the Spurs do this:
Not gonna explain why they'd want to move off from Fox, check my previous Fox trades for the reasoning. With this trade, they immediately have the best starting lineup in the league, as well as helping out their bench a bit. Their current roster needs are a PF with some size who can defend and shoot (PJ fits perfectly) and a backup C to hold the team down when Wemby's off (Gafford). They could also use someone with a lot more scoring and shot creation ability, particularly in clutch settings, as Fox proved not to be that. Kawhi, being a clear top 10 player who can fit with any team, instantly makes this Spurs team the favourite to win.
In terms of what they're giving up, its quite a lot, but absolutely worth it to improve their roster so drastically. Fox and Keldon won't be missed all that much and should both be on the move anyway. Vassell was fantastic for them throughout the playoffs, so that one will hurt, but they're swapping him out for a top 10 player who can do all the same things at a much higher level. Carter Bryant could end up being a great player, and its a shame to lose him, but worth it overall. The picks could be of great value, particularly the Atlanta 2027 first, but they're not giving up any of their own in this deal. Overall worth it for the major roster improvement, as well as getting off Fox's contract and bad fit on the team.
Why the Clippers do this:
Kawhi is probably at his peak value right now and won't be worth more if they hold onto him any longer. The Clippers aren't in a legitimate position to contend, and with them now having a solid cast of younger players, they should look at seriously rebuilding. Kawhi is still good enough to play on a contending team and would be wasted on a rebuilding one. With this trade, they get back some solid players, including an intriguing young guy in Carter Bryant, and a pick that, with the new lottery odds rewarding play in teams, could end up being very valuable. Vassell and Johnson can be long term pieces or they could be flipped at the deadline or another time, either way good additions.
Why the Mavs do this:
This is all assuming they look to trade Kyrie. With that being the case, they'd be completely devoid of a point guard. Fox would raise their offense and pace pretty drastically, and would really help guys like Flagg and Morez Johnson in that way. They're giving up Washington, Gafford and Martin, three guys who would most likely be coming off the bench for them next season anyway, and getting some good value out of them. Fox's contract might be pretty awful, but they're also shedding a good amount of long term money in Gafford (3 years left on the contract) and Washington (4 years left on the contract). Fox's contract will overlap with Flagg's post rookie contract extension for one year, and won't overlap with Morez Johnson or any other younger guys they might draft/trade for. They would get more value out of Fox than most other teams, and his contract affects them less than most other teams. The pick compensation also helps, but I'm open to other picks being included too.