You were using the Mac disk utility as you wanted to create a new partition to store some data separately. But while the partitioning was in the process it was abruptly stopped by some error and the partition got failed. Sometimes the impact of the Mac disk utility partition failed error is just minor and you can try to repeat the process again but sometimes it can corrupt the whole Mac drive. You will again have to use the disk utility to fix the corruption, however it may not be always capable of fixing the Mac drive. In that case formatting the drive is the only option, which may fix the Mac disk utility partition failed error but also deletes the data that is stored in the drive. You can get back the images from the Mac drive when the time machine backup is working and has all the copy of files that you need. If the time machine is not working then you can use the Mac data recovery software which is do its job perfectly. The software needs to be installed then scan the drive to get the files back. So don't wait much download the software after you fix Mac disk utility partition failed error.