As has been pointed out by Stefan, there's no need to cut any mud blobs (red tar = mud). But I think that even if you choose to cut one, the solution will still be similar...
The problem you have is that the mud fills all entrances to the box. Think what can you do to prevent the mud from growing into one of the passages after the red doors are open. Hint: obviously, you know that the mud can grow only on free tiles, right?
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×Collect enough mud babies below the southern red door. When you drop the last trapdoor they'll get inside. They'll occupy some tiles and thus reserve you a 1-tile passage the mud cannot grow onto.
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×Once you've dropped the last trapdoor, don't hurry back. Stay there for awhile to let the mud mother blob grow and lock the mud babies in.
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×Also you would need to kill the mud mother before you cut your way into the seep box, otherwise you have good chances to stay there forever.