You can, however any time you sample a part of a recording you did not record yourself, you MUST have a license from the owner of that original recording. You cannot distribute any content through TuneCore that you do not hold 100% distribution rights for.
Songs where you sample other recordings can get very tricky as you are often required to purchase a master use license from the label or publishing company which holds rights to the original recording. (Sorry, TuneCore cannot provide you with any direct label contact information).
If you have any concerns at all that you may not have rights to any audio in a remix, mix tape or mashup you're uploading, please do not upload that song(s) to TuneCore.