"stumbling over words" is a correct and usable phrase in written English.
It is typically used to describe someone who is having difficulty speaking or articulating themselves, often due to nervousness or lack of fluency. Example: During the presentation, the speaker was stumbling over her words, unable to clearly convey her ideas to the audience.
They read aloud haltingly, stumbling over words like "Vietnamese," "fatalities" and "authorities".
He reads awkwardly at first, stumbling over words like "Buccleuch"; his co-workers mill around, sorting mail, looming behind windows.
She reads from a crumpled piece of paper, stumbling over words in a language she has learned late in life.
Rather, it was the delivery -- the stumbling over words, the compulsive ear scratching, the mumbling and sudden laughter -- that left the devastating impression of a prep-school kid striving for a B in public speaking.
The machines became a point of attack in the blogosphere, with one critic even setting up a Web site called teleprompterpresident.com to post videos of the candidate stumbling over words when he did not use the machines.
Then she recites, with hardly any hesitation, or stumbling over words: "'She waited, Kate Croy, for her father to come in, but he kept her unconscionably, and there were moments at which she showed herself, in the glass over the mantel, a face positively pale with the irritation that had brought her to the point of going away without sight of him.
Jellinek was nervous and several times stumbled over words.
Occasionally he can still stumble over words but he delivers a plainer message in plainer language.
Much of the document was handwritten, and Stewart stumbled over words as he read it aloud.
At first, the candidates stumble over words; they repeat, "absolutely" too often, or stare at their feet too long.
He stumbled over words, mixed metaphors, forgot lines and went back on himself – and the audience drifted from his grasp.
