Backdash Attack
A trait unique to SSJ Goku (and Base Goku, and later TenShinHan got it too), he can perform one of his jumping attacks while backdashing.
Flurry Punch / Fury Uppercut
Goku performs a flurry of quick punches while slightly moving forward and ends with a punch to the gut. This can chain into his Special or Super moves. Pressing Strong Punch again makes him perform the Fury Uppercut, which launches the opponent, setting them up for an aircombo.
Blur Max Kick Combo
Pressing Strong Kick three times in a row (when they connect, of course) makes Goku perform a short series of kicks. The last kick is a combo-ender, knocking the opponent away. If you caught the opponent on a counter hit with the first standing Strong Kick, the last kick in the series gets buffed a bit and and causes a wall bounce. You can combo into Specials / Supers after the first or second kick. You can also combo into this series of kicks from the running kick attack which is detailed below.
Uppercut
Main launcher tool. After hitting the opponent with it, press Up to pursue them and set yourself up to perform an aircombo.
360 Splits Kick
Due to its jumping nature this attack has some invulnability on Goku's lower body at the start of the animation. You can't really combo into any of his other moves after this hits except when using a Teleport and the timing on using it correctly with this move can be tricky.
Boomerang Kick
Main tool for smashing opponents down to the ground during an aircombo. If an aerial opponent is hit by this move, they'll fly to the ground and bounce up upon impact, allowing for a juggle combo.
Turn Boomerang Kick
Works identical to the regular version, feature-wise. This reverse version is useful when superjumping over an unsuspecting opponent and striking them over the head from behind with it.
Wing Kick
Spinning overhead attack, since it's a running attack it can cancel out of your Focus Attack. This can chain directly into standing Strong Kick and thus the Blur Max Kick Combo.
Ki Blast
When used in conjunction with his teleports this becomes a dangerous combo/mix-up tool. Goku fires a basic Ki Blast straight forward. The speed the blast travels at is determined by the strength of the button input: Weak version travels slowly, while Strong version travels fast. Medium as usual is somewhere inbetween. You're able to shoot out three of these Ki Blasts consecutively by just pressing forward+any Punch up to two times after doing the first one with QCF+P. You can mix up the Weak and Strong versions. Supercancelable on hit. The EX version becomes the G-Pressure / Invisible Ki Blast, which is a very fast-traveling, invisible energy attack that knocks the opponent back on impact and into a wall-bounce. It has a combo limiter; performing the G-Pressure a second time in the same combo knocks the opponent away in a twist knock out and won't wall-bounce them again. You're able to cancel into the EX version either after the first, second or third Ki Blast. You would do so with the command forward+2 Punches. The stand-alone version would be done with QCF+2P
Blast Fist
A special move adapted from Goku as he appeared in Super Dragon Ball Z. It's a Shoryuken-type jumping uppercut that does multiple hits and causes explosions on impact. It's fully invincible through the first hit! The Weak version rises only a little bit, while the Strong version reaches well above the edge of the screen. The EX version does even more hits and damage. You can supercancel into his aerial (Super) Kamehameha during or right after the rising hits. You can also cancel into one of his special Teleports at any time (though not if the attack was blocked).
High Speed
Goku performs a quick forward dash during which he can switch sides with the opponent if he's close enough. That'll confuse them!
Slash-down Kick
SSJ Goku's dive kick is now updated, he'll now first teleport to a certain position in mid-air (by using the LK, MK or SK version), then dive-kick down. Upon hitting the opponent, you can choose to land and then start a basic combo string, or supercancel into his aerial Kamehameha. Because of the teleport, all versions now have the same angle coming down. The EX version hits three times. When the EX version is blocked, Goku recoils backwards a bit.
Miracle Strike
This move makes Goku dash forward, colliding with the opponent if they come into his path, then he smashes them down to the ground with a big overhead punch. They'll slide across the ground for a bit until they come to a stop You are able to cancel the rising part of the Blast Fist into this attack.
Teleport
SSJ Goku overall has fewer Specials compared to other characters but the Teleport is one funky tool that opens up a whole new book of combo possibilities. Below the Power bar, Goku has a small bar with an icon of himself doing the Instant Transmission pose beside it. Let's call this the Teleport Stock Bar. It can hold up to two stocks of Teleports. After using a Teleport, a stock is drained but it will keep refilling over time automatically.
The Teleport is an EX-only move so it always costs 1/2 of a LV1 to use. It only costs this outside of Justice Mode though. A Teleport with Punch inputs places Goku on various spots on the ground, while a Kick-teleport places Goku in mid-air. This is also true for when the Teleport is activated in mid-air.
There are three versions for each variant; Light (nearest range or even going backwards), Medium (farthest range) and Strong (inbetween). And there's 4 variants (Punches on the ground, Punches in the air, Kicks on the ground and Kicks in the air), so 3x4 makes 12 variants! Wrap your head around that.
Also, when a Special Move is blocked, you can't teleport cancel out of it. You can only use one Teleport cancel per combo, though this increases to 2 uses when in Justice Mode.