silence a buffed and damaged minion will not affect the buff on its hp?

First turn: My opponent played 8/8 mountain giant, I attacked him to 8/1.

Second turn: My opponent played Shattered Sun Cleric which gave mountain giant +1/+1, now Mountain giant is 9/2.

Then it's my turn, I played Ironbeak Owl on mountain giant, theoretically it should set back to 8/1 since I silenced buff, but he actually got back to 8/2. Why?

Solution 1:

Any effect which increases maximum health also increases current health.

Any effect which decreases maximum health does not affect current health, unless the new maximum health total would be less than current health, in which case current health is set to maximum health.

In your example, the silence effect decreases maximum health but doesn't affect current health because its maximum health of 8 is still greater than its current health of 2. However, if you subsequently used a Hunter's Mark on the giant, it would lower its maximum health to 1; since the giant's current health of 2 is greater than its maximum health of 1, the current health is lowered to the maximum.

See also this forum thread.