Jie, from China, topped unseeded Estonian Kaia Kanepi, 6-4, 6-4,. Arvidsson beat fellow Swede and wild card Johanna Larsson, 6-2, 1-6, 6-4.
In Friday's quarterfinals, top-seeded Anastasia Myskina of Russia will face Martina Sucha of Slovakia; No. 2 seed Na Li of China meets Tszvetana Pironkova of Bulgaria; Jie plays Wozniacki; and Arvidsson will play Birnerova.
Myskina, the 2004 French Open champion, was last year's Stockholm runner-up to Katarina Srebotnik of Slovenia.
Sunday's champion will claim $22,900.
Swim Week Miami Beach 2014 [PHOTOS]