Click Edit > Paste Special > Paste as unformatted text Ctrl+Alt+Shift+V. I have added the Paste as unformatted text icon to the Standard toolbar as an extra assistance. Note that for Calc this won’t paste formulas.
An alternative is to paste normally, then select the pasted cells in Calc or text in Writer and press Ctrl+M to remove direct formatting. For Writer you might still need to change the style of the pasted text, so still with the selection, choose your paragraph style. Pressing Ctrl+0 will convert it to Text Body which is intended for normal writing. Also, Ctrl+1 for Heading 1,Ctrl+2 for Heading 2, & Ctrl+3 for Heading 3
More information on styles can be foud in the Writer Guide, free download from English documentation | LibreOffice Documentation - LibreOffice User Guides