I wouldn't say SDA's are denying th existence of the HS as much as they are denying the explicit personhood of the HS. The Bible is clear that the Holy Spirit exists; but (to me at least) it is also clear that the HS in the Spirit of Christ, or the Spirit of God.
"You, however, are not in the realm of the flesh but are in the realm of the Spirit, if indeed the Spirit of God lives in you. And if anyone does not have the Spirit of Christ, they do not belong to Christ." (Romans 8:9)
"And if the Spirit of him who raised Jesus from the dead is living in you, he who raised Christ from the dead will also give life to your mortal bodies because of his Spirit who lives in you." (Romans 8:11)
"And that is what some of you were. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God." I Cor. 6:11)
"You show that you are a letter from Christ, the result of our ministry, written not with ink but with the Spirit of the living God, (II Cor.3:3)
"for I know that through your prayers and God’s provision of the Spirit of Jesus Christ what has happened to me will turn out for my deliverance." (Phil 1:19)
"Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters." (Gen. 1:1)
See also Gen. 41:38, Ex. 31:3 and 35:31, Numbers 24:2, 1 Sam. 10:10 and 11:6, 2 Chron. 15:1 and 24:20, Job 33:4, and Psalm 106:33 for just a small sample of scriptures pointing to the HS being the Spirit of God or the Spirit of Christ.