The slime will coat all floor, ceiling, and walls in the area, so even if you save successfully and get no patches on you, you still have to deal with any on the floor in your space, plus any on adjacent walls or the ceiling which will fall onto you.
While it does not say what action you would need to take to scrape off a single patch, I would make it a full-round action, akin to the kind of action required to extinguish a fire if you are burning. The scraping item would take damage from the slime, based on its material. So, a wood or stone scraping tool (shovel, weapon, shield, etc) would be damaged by the slime, while a stone tool would be unharmed.
For cutting it away, a full-round action again would be appropriate, as you do not want to risk missing any or cutting too deep. Damage to the person affected should be appropriate to the weapon's base damage, and ignore any feat or strength bonuses, because you are not attempting to attack at full power.
Fire or cold, any damage would be sufficient to remove a single patch. An AoE (such as Burning Hands) would be required to remove multiple patches at once. Daylight is not sufficient for removing green slime, as Daylight does not simulate natural sunlight, but Sunbeam or Sunburst would work.
Using the spell in any place lit with sunlight would cause the spell to essentially fail, because the slime is destroyed before it can affect anything.
One final thing I recommend: against undead, corpses, and bone implements, the slime deals 2d6 damage per round per patch, because there is no Constitution to affect, yet the slime eats away at those materials.