Do whatever is better for communication:
- If it's fast paced and and everybody follows the thread just type you answers. If you are referring to many points you can quote the each point before adding your input for clarity. You can remove original message.
- If it goes slowly and many people are involved you may consider keeping the history. You may need it to catch up after a longer break or others may need it to understand what is it all about.
Note that a single photo takes a couple dozen kB, word and PDF files few hundred.
How much text only email history takes? Usually no more than a few dozen kB and if it gets really lengthy you cut cut off unnecessary/old parts or start a fresh thread but I don't think you should bother.
Your and others' time and clarity is worth much more that space you can save. You can easily get at least a gB to store you emails for free which is 1000*1000 kB!
If you really think you need to save space I would recommend deleting old thread attachments. Or maybe uploading attachments somewhere else and sending links only. But seriously in most of the cases if you don't have enough space for your emails you should either backup old stuff or get extra space.
Just remember, work time and clarity is worth several time than extra space.