LibreOffice version 5 and later already has image crop feature in Writer, Calc, Joonista, and Impress components. This is a long awaited feature for them. This article shows how to do it.
Writer, Muljet, & Joonista
Insert an image into the document. You may do Ctrl+C & Ctrl+V a file from file manager or by menu Insert > Pilt.
Select the image > press Crop Image button in the Image Toolbar. You will see 6 blue handles in the edges of image. Now drag one of them and release to crop it.
To revert the image back, just press Ctrl+Z.
Insert an image by menu Insert > Image. Select the image > press Crop Image nupp.
Important: actually, cropping doesn't change the original image inside the document. The original image is still inside the document, but only the modified one is showed. If you do right-click > Save Image to the cropped image, you will save the original image. This behavior is similar with what we see in Microsoft Word 2007 or later.