Please tell me can getting tooth extractions for braces affect your face?

Ortho extractions: The aim of proper Orthodontic treatment is to strive for an ideal occlusion (bite) and an aesthetic smile and facial contours. If removing some teeth is deemed necessary and beneficial, the result should not adversely affect your face. This is an issue that you need to discuss with your own Orthodontist prior to treatment so that you understand why it is recommended.

Yes it can: Extractions can change the support of your lips. If your lips are too pushed out and they don't close easily, extractions will improve your profile. If your lips are already too far back your doctor must be careful not to make that worse.

Definitely, yes: It can change your face for better or worse. However, In most cases there will be no perceivable change at all. See a board-certified orthodontist for second opinion before orthodontic treatment.