It sounds like the Tascam can't do what you want it to do. It only burns 'closed' CDs, so the data is fixed and can't be changed once it's burned. All you can do is load it back onto the machine, add more tracks, mix them down and burn them to another CD. Also, if you can't wipe the CD-RW on the Tascam, and you don't have access to a PC with appropriate software on which you can wipe the disc, then the "rewritable-ness" of the CD-RW is lost to you. You can only use it exactly as you'd use a regular CD-R.
A CD-RW is only rewritable used this way: you write to it, wipe it, then re-use it again as a blank CD. You can't add more data to it in the way I think you want to do.
You can only add more data to a CD which has been left 'open'. You don't need a CD-RW for this, you can do it with a CD-R. However, from what Dunder XIII has said the Tascam can't do this. So that is the problem: the Tascam can't write CDs in 'open' format.