Voice Memos doesn’t have a fully-featured audio editing suite (for that, you’ll need to use GarageBand), but you can quickly trim the audio or delete parts of the recording.
Select the voice note, tap the three-dotted Menu button, and choose Edit Recording. Then tap the Edit icon in the top-right corner and use the yellow handlebars to select the audio. If you want to remove what you have highlighted, tap Delete; if you want to only keep the selected part as the audio, choose Trim. Once you’re done, tap Save, and Replace if you want to save over your original file.