整个句子有没有问题

有的。最后不应该再用it.
因为实际说的就是you can deal with the specific time,再用it则与the specific time重复，故产生语病。
这里you can deal with 是做the specific time的后置定语，用来修饰time的。

相信我，没错的

specific time - 用 when
如果是 a period of time 一段时间/时候，
才用 which, that

如果前面有could you tell me这个句子，后面跟的句子要用正常语序，即which the sprcific time is

but could you tell me which the specific time is you can deal with it?

为了句子读起来不像中式英语，建议你直接说could you please tell me at what time you can deal with it?

不通顺，可能有问题。是否可改成：but could you tell me the specific time you can deal with.

but could you tell me the exact time when you could deal with it.

没有问题，宾语从句中含有定语从句。