Yes, it is grammatically correct, assuming you are referring to something masculine — or a person or animal of unknown gender.
If you want feminine or neuter, or perhaps a plural of some gender, you will need to change the endings.
If you want something with the stems caed- and claud- instead of the -s- in the perfect stems, then I would suggest caedor et claudor ("I am cut and closed") or caeditur et clauditur ("he/she/it is cut and closed").
These are different to use since these are personal forms instead of participles.
It is also possible to mix, like caesus claudor ("I am closed when I am cut"), but then the two verbs are not on equal footing.
Yet another way to vary the motto is to use -que instead of et (see this question for a comparison), as in caedor claudorque.
The real trick is in choosing the words with the most suitable meanings.
Take a look in Lewis and Short at caedere and claudere to get more details than Wiktionary gives.
I can't judge whether they mean exactly what you want, but they look like reasonable choices to me.
If you don't like the way it looks, you can try any of the numerous other online Latin dictionaries.