Can I connect my laptop's (VAIO model VPCEB26FG) hard disk to my desktop's SATA cable and to desktop's power cable supplied by SMPS and take data backup? Or does it cause voltage issues and damage the hard disk? Please explain what happens.
You can put your laptop drive in your towers power and sata plugs. Your looking to see if the power supplies design for efficient power use will harm the HDD. It will not.
The SMPS is performing on off cycles (very fast) to eliminate energy loss. The load to the computer and other attachments, including hard drives are not affected by this.
As SATA signal/data connectors are standarized, so - if you match connectors - SATA data connection will be compatible.
SATA power connectors are standarized too. However, to be completely sure of the power cable compatibility - it is general rule for electrical appliances - you should look at HDD rating plate (part of HDD sticker):
If your HDD allows power cable voltage it will be OK.