Bricked my Xperia SP in CWM recovery It seems like I have bricked my phone. I have installed CWM recovery, and I accidentally wiped all the data it had. Now I can do nothing with it. 

When I choose "mount sdcard" it says "error mounting sdcard". I was trying to install cyanogenmod, but I didn't find any update.zip in the downloaded file (I have followed the tutorials in their official site). 

How can I fix my device? I don't want to throw away my brand new shiny phone :(
If your phone won't mount your SD card, there are a couple of recourses. Take faith- as long as CWM is working, your phone is not really bricked- just soft-bricked.
If you haven't installed ADB on your device, you'll need to for this method. I'd recommend Minimal ADB and Fastboot for this.

So I have the answer to at least part of your problem. The "update.zip" file doesn't exist- in the instructions any instance of that should be replaced with the version of Cyanogenmod you downloaded- for example, cm-11-20140923-NIGHTLY-huashan.zip.
Per the instructons here:

"Push and install method: Open a command prompt (or Terminal on Mac and Linux) and navigate to the directory holding the package(s) you would like to install. On the device, navigate to the mounts and storage menu. If you see /storage/sdcard0 as a mountable volume, go ahead and mount it. If you do not see this directory, then instead mount the /data directory. Take note of which volume you mounted. 

Now, push the package(s) to your device:


If you mounted /storage/sdcard0, then: adb push update.zip /storage/sdcard0/
If you mounted /data, then: adb push update.zip /sdcard/0/


where update.zip should be replaced with the package filename. Go back to the main menu and select install zip. Choose to install from the same directory where you pushed the package(s). If you are installing multiple packages, install CyanogenMod first and then install any subsequent packages on top of it."

If you still have issues mounting the storage, please reply. I'd be happy to help.