I attack with a creature, opponent declares a 1/1 as blocker. Can I kill the 1/1 right before blocking happens, therefore allow my attacker to go through?
Once a block has been declared the creature will remain blocked until end of combat no matter what happens to the blocker. You would need to kill the creature before blocks are declared.
Before blocks are declared, you have no information about what the opponent will block with, apart from inferring from restrictions and requirements generated by effects applicable at that time. Your opponent commits to nothing yet. If you remove one creature here, the opponent may block with another when that time comes.
After blocks are declared, they actually happen. It is part of the turn-based action of the declare blockers step; nothing intervenes between declaration and performance. Once creatures have blocked, attacking creatures that were blocked become blocked creatures, and blocked creatures, for almost every situation possible to construct with legal, black-bordered cards in Magic, do not become unblocked creatures again in the same combat. They won't "go through" without gaining trample.
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I attack with a creature, opponent declares a 1/1 as blocker. Can I kill the 1/1 right before blocking happens, therefore allow my attacker to go through?
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After blocks are declared, they actually happen. It is part of the turn-based action of the declare blockers step; nothing intervenes between declaration and performance. Once creatures have blocked, attacking creatures that were blocked become blocked creatures, and blocked creatures, for almost every situation possible to construct with legal, black-bordered cards in Magic, do not become unblocked creatures again in the same combat. They won't "go through" without gaining trample.
Awesome avatar provided by Krashbot @ [Epic Graphics].