Magic The Gathering; Do "target loses -x/-x until the end of the turn" counters destroy a creature?

As a state based effect, all creatures with toughness less than 0 is put in the graveyard and no player can respond to state base effect. You are not 'sacrificing' your 2/2 soldier. The game check for state based effect whenever a player has priority. Your 2/2 dies due to an activated ability and because Guul Draz Assassin's is an activated ability, you can respond to it in order to save your creature.

Detail:

Your opponent pay {B} and tap his Assassin targeting your 2/2 soldier for a -2/-2. Once the activation cost is paid (the black mana and tapping the Assassin), the activated ability "Target creature gets -2/-2 until end of turn" is put on the stack waiting for response or to be resolved. In respond while this ability is on the stack, you can cast buff spells like Giant Growth. Now, Giant Growth is put on the stack and becomes the top most item on the stack. Assuming nothing else happens. The stack starts to resolve each ability or spell starting from the top most item; in this case, your Giant Growth. When Giant Growth resolves, your 2/2 gets +3/+3 until end of turn. Once Giant Growth resolved, your soldier is 5/5. Now the Assassin's ability resolves and your now 5/5 gets -2/-2, and therefore, it becomes 3/3. Assuming nothing else happens for the rest of the turn. At the end of the turn, all damage and "until end of turn" effect is clear at the same time. So your soldier becomes a 2/2 again.

Any time a creature has 0 toughness or less, it is sent to the graveyard as a state-based effect. It is not sacrificed (so it doesn't trigger effects like Mortician Beetle), and it is not destroyed (so Indestructible and Regenerate cannot protect against it). It doesn't matter if the cause of it having 0 toughness is temporary ot not.

Also, Ghul Draz Assassin and similar effects don't put counters on the target creature, they directly modify the base stats of the creature. This is significant in the case of a creature with +1/+1 counters on it that survives the effect.

If your creature becomes a 0/0 then it dies right away. It is not sacrificed, state based effects see a 0/0 in play and send it to the graveyard. You cannot respond to state based effects so you cannot stop it from going to the graveyard.

A ruling on similar cards from 8/1/2008 says: A noncreature permanent that turns into a creature is subject to the "summoning sickness" rule: It can only attack, and its {T} abilities can only be activated, if its controller has continuously controlled that permanent since the beginning of his or her most recent turn. Rule section 302.6 of the comprehensive rules indicates that "A creature can't attack unless it has been under its controller's control continuously since his or her most recent turn began." So if the land was in play at the beginning of this turn, or you have some way of giving the land haste (ala Anger; see sources) then the land can attack.

Whenever a creature has a toughness of 0 or less, it's put into tge yard as a state based effect.

Your creature dies immediately. Not even a sacrifice. It's destroyed as a state-based action. this overrides even abilities like Indestructible.

It dies and is not sacrificed.