Port mirroring (SPAN, RSPAN, RAP and so on) typically copies traffic at a packet level. You can only bypass it on a similar or lower network level. Depending on how mirroring is configured, this means you would have to use different physical layer connection (e.g. wireless hotspot) or route packets to bypass capture point (bridging, vlans).
Now, port mirroring would not magically decrypt your traffic. For example, if you create VPN tunnel and route all your traffic through it, such capture will be entirely useless in determining what is being sent, but it is still possible to determine endpoint you VPN to and how much data and when it was sent. If you use HTTPS, then it will be possible to determine what websites you visited, but not what you did there (e.g. checking gmail - they won't be able to read your email with just port mirroring). If you just use HTTP (e.g. posting on stack exchange), then it is possible to see in the packet capture not only that you visited here, but actually what you posted.