In the process of learning to play, it can be overwhelming to deal with all the options a character has at any given moment. To get a better handle on how to use each option, it can be helpful to limit yourself to only a few options in order to demonstrate a certain principle about the game. Some of these can also serve as handicaps for stronger players
Sweep and Throw
One of the simplest mini-games that demonstrates a number of things about how to play the ground game, and how to punish moves. Basically, restrict yourself to staying on the ground, and only using sweep and throw. You can walk, you can dash, but no jumping. Sweeps are unsafe on block, so if you block your opponent's sweep, you can usually sweep them back. This teaches good sweep spacing too, because hitting with the tip of a sweep can make it safe by pushing the opponent too far to punish. Sweeps also serve as pokes keeping the opponent out of throw range. This game has a lot of nuance, like sweeping to keep the opponent out of your face, but they can move into your range to provoke a sweep on purpose so they can block and punish it. It can also teach whiff punishing, as people want to naturally sweep with the tip of their foot, but if they're out of range their opponent can hit their extended hurtbox. If you sweep safely at range, and the opponent tries to punish on block, it can force a whiff that can be punished as well.
Jump-in / Fireball / Anti-Air
In this Mini-game, focus on your zoning game, and beating the opponent's zoning game. This game also works if one person takes the role of zoner, and the other the role of attacker, and you switch every so often. The idea is, the zoner shoots fireballs to keep the opponent out, and anti-airs them when they jump, so the non-zoner needs to learn the right timing to jump fireballs, and get good at reading when they'll be thrown to avoid getting anti-aired.
Pick 3 Buttons / Only Lights
In this game, a weaker player picks 3 buttons for their opponent to use. The stronger player can only use those buttons, and specials tied to those buttons. As a variation, the stronger player can only use light attacks, and maybe the specials associated with those light attacks. Light attacks deal significantly less damage than other moves and have shorter range, so even though the stronger player is much more capable of landing moves, they're inhibited by low damage, no combos, and short range.
Shoot for Timeout
In this Mini-Game, a stronger player attempts to deliberately only go for timeout on their opponent. Any rounds won by damage as losing the whole match for the stronger player. This puts a balance on how much damage the stronger player is willing to do. If they go all-out early on, they can find they have few options to fend the weaker player off without accidentally killing them, making it tough to wait out the remaining time. It can also help coax weaker players into going for throws and anti-airs more often, as the stronger player is incentivized to jump and block to avoid damage.
In this Mini-Game, no using combos longer than 1-2 moves (Not hits, since some moves naturally combo). Limiting it to 2 rather than 1 can help with canceling into specials, and making jump-ins more rewarding. If you accidentally go over the limit, offer your opponent a penalty hit/combo for free. This mini-game can help handicap a stronger player, since combos allow stronger players to get much bigger damage off individual hits than
First to Corner Loses
What it says on the tin, first person to have their back to the corner loses. This mini-game teaches you to utilize space efficiently, and be wary of walking backwards, jumping backwards, and backdashing, as all may be good at avoiding damage, but put you closer to your lose condition. If you run out of health, then you lose same as normal. If you get cornered, you can just throw the round to make things simpler.
As a variation, you can do this mini-game with no jumping allowed, to train the ground game. This can be more intense as you don't have an easy way to gain more ground by jumping forwards over your opponent.
One player blocks in the corner, the other tries to break their defense without using throw. Do this for 30 seconds, award points if they last for the time limit. Take turns being the blocker or attacker. This is more of a drill than a Mini-Game, but it's helpful if you have 2 people for it. It can help teach people to block highs on reaction, and to block low after a jump-in.
Jump Attacks Only
One player is only allowed to hit with jumping attacks (and maybe combos off jump). The other player can do whatever. This can be a good handicap for a stronger player who knows to vary their timings on jumps and jumping attacks, and mix in ground movement. Teaches beginners to block crossups, and to anti-air consistently. A variation might be to require the other player to stay grounded, to avoid devolving into just air-to-air battles.
One player can only use Shoryuken. All normal movement is allowed, but the only attack allowed is a Dragon Punch type of move. This is especially effective with characters who have a quick recovery on whiff for Shoryuken, like Ken in most Street Fighter games. This teaches beginners to block and punish shoryukens, as well as whiff punish them. this is probably best suited as a handicap game, as better players will have an easier time staggering their timing on shoryukens and picking the right one for the right situation.
Play this game in the training room. Knock one player down (the defender), then the other player (the attacker) attacks them on wakeup. If the defender is overhead hit or thrown, the attacker gains 1 point. If it's a low or medium hit (one that would start a combo), they gain 2 points. If it's a jumping hit they gain 2 points. If the defender successfully blocks, they gain 1 point. If the defender does a reversal that hits their opponent they gain 1 point, but if their reversal is blocked/whiffed and punished, the attacker gains 3 points. A defender successfully interrupting the opponent's pressure to score a hit or throw gets 2 points. A round ends after a player is hit, or the situation resets to neutral (you'll have to use your judgment on this for things like frametraps, block strings, and tick throws). Then switch the attacker and defender and play another round. Add up whoever has more points after 3 rounds or more.
This is a condensed version of the wakeup game that is played commonly with point values to help make it clear who won or lost each exchange. As an optional ruling, you may want to have sweeps and throws only score 1 point, but give you another turn as the attacker. The points are weighted to hopefully make blocking low edge out the other options, since it's slightly more rewarding than in a real match, and to make reversals high risk low reward, like in a real match.