In the construction "[get] + [direct object] + [past participle]," the past participle is always used.
I'd like to add that a present participle (V-ing) may be found after the direct object in very few, highly idiomatic cases like "get it going." In such cases, the meaning is active, that is, the action is to be performed by the object. These examples have been taken from the Longman Dictionary of Contemporary English:
get something doing something (make something do a particular thing) e.g. We got the lawn mower working again eventually.
get somebody doing something (persuade or force somebody to do something) e.g. In the end, we got the children clearing the playground.
In both of the cases above, a "to"-infinitive can also be used with the same meaning:
- We got the lawn mower to work again.
- We got the children to clear the playground.
However, the causative construction get + direct object + past participle (where the past participle has passive meaning, because the direct objec is affected by, and does not perform, the action) is much more usual. In your example, bear_bear, "get it completed" is in fact the only possibility, as David rightly told you.