Need some help

I'm building a mono amplifier to use with a bass speaker.
I have one question. I will connect it to tape out on my stereo amplifier (I will have a separate volume control). Can i connect right and left to each other to make it a mono signal or will that damage the sound/amplifier in any way?

DO NOT do what you are thinking about!! This will damage your equipment!!! You are effectively shorting the left and right channels together. You may want to find a dedicated subwoofer amplifier that will sum the signals from the left and right channels and then amplify that sum. You cannot achieve the same result by simply shorting the outputs!
I don't know that I'd go so far as to say that it will damage your equipment; most line level sources can be wired together without harm. However, it would be more graceful to sum them together through a resistive network. Better still would be to have an active buffer.
Keep in mind that what you're proposing will drive you crazy in short order because the level of the tape output will not vary. Every time you change the volume, you will need to rematch the volume of the subwoofer. If the phone rings and you turn the volume down, the subwoofer will still be thumping merrily along. It's up to you.