If I need to withdraw $1,000 from StashAway, does it mean I can get $1,000 or will there be some tax deduction/processing fees?

As per Stashaway FAQs:

"Do you charge a fee if I withdraw funds from my StashAway account?

Nope! It’s your money, and you should be able to access it easily. StashAway will never charge you if you want to withdraw money from your account. However, if you are withdrawing your money to an international account outside of Singapore, your bank may charge you conversion fees. Additionally, your bank may also charge you a fee for receiving overseas telegraphic transfers - this fee varies from bank to bank and will be automatically deducted by your bank from the received amount."

Hope this helps!