No, a character cannot perform two top actions or two bottom actions in the same turn.

This is explicitly stated in the rules:

• "On a character’s turn, unless performing a long rest (see p. 38), they will perform the top action of one of their played ability cards and the bottom action of the other. They cannot perform two top actions or two bottom actions."
  (page 34)

• "A character cannot perform two top actions or two bottom actions."
  (page 76)

Therefore, each turn (unless long resting), a character must perform one top action and one bottom action from the two cards they played.

Source: pages 34, 76

Source: Core Rulebook (pp. 20, 34, 37, 38, 76)