When I play Twhonk and repeat the effect, can the spell card Defy Negate the mine effect?

Yes, Defy can negate the entire Thwonk! spell, including its Repeat effect.

According to FAQ #256 and FAQ #426:

• When you cast a spell with Repeat, you must choose whether to pay the Repeat cost at the time of casting, before your opponent can respond.
• If you choose to Repeat, the Repeat effect is part of the same spell on the chain.
• If your opponent plays Defy to counter the spell, it counters the entire spell, including the repeated portion. You cannot wait to see if your opponent Defies before deciding to Repeat, and Defy stops the entire effect.

Sequence:

1. Declare: You declare you are casting Thwonk! and choose to pay the Repeat cost as an additional cost.
2. Finalize: The spell (with its Repeat effect) is finalized on the chain.
3. Respond: Your opponent plays Defy as a reaction to your spell.
4. Resolution: If the Defy is successful, the entire spell (the base Thwonk! effect plus the Repeat effect) is countered and placed in the trash.

Note: Per Rule 412.1.c, countering does not refund any costs paid to play the card, including the additional cost paid for Repeat.