With Collection.Find() you can only specify the filter. But what you have is a projection:
{"contr":{$slice:[0,10]}
Projections can be specified using Query.Select(), so this is how you can apply a $slice in projection:
var results []bson.M // Use your own type here, but this works too
err := DB.C("con").Find(bson.M{"id": ID}).Select(bson.M{
"contr": bson.M{"$slice": []int{offset, limit}},
}).All(&results)
// handle error
Also note sure if the property you filter by is "id" or is just a typo and it should be "_id". If the latter, you may also use Collection.FindId() to query by document ID:
err := DB.C("con").FindId(ID).Select(bson.M{
"contr": bson.M{"$slice": []int{offset, limit}},
}).All(&results)