Differences between the two

Grammatically both the two are correct.

The word almost means to very nearly.

The first one tells about loosing about one full pint of blood........... while the second one tells that you have saved it.

Saved, while correct, carried a British English connotation and is not frequently used in American English. The American English interpretation:

"lost almost a full pint" --> you DID lose blood, and the amount lost was nearly a full pint.

"almost lost a full pint" --> might mean exactly the same as the first, OR it might mean you MIGHT HAVE (under different circumstances) lost blood.  In American English, we are likely to understand it the same as the first because of the use of "full".  If you had narrowly averted losing blood, you would not know how much blood you might have lost. You would say "I almost lost blood, but I was lucky to escape with just a bruise."